clase Astrid 2 de secundaria "sacar le ecuacion a partir de una grafica
profe Alberto Argon
[{'start': '7.707', 'end': '15.982', 'text': '>> Professor Alberto Argon: Okay'}, {'start': '9.809', 'end': '16.483', 'text': ">> Daniela Rojas: Okay, let's go"}, {'start': '14.848', 'end': '19.786', 'text': ">> Professor Alberto Argon: Let's"}, {'start': '15.448', 'end': '19.786', 'text': 'see how'}, {'start': '16.049', 'end': '19.786', 'text': 'we can get the'}, {'start': '16.549', 'end': '19.786', 'text': 'equation from a graph.'}, {'start': '20.887', 'end': '28.828', 'text': 'Look here is the graph.'}, {'start': '31.931', 'end': '40.840', 'text': 'And from this graph'}, {'start': '35.969', 'end': '40.840', 'text': 'we are going to get the'}, {'start': '36.436', 'end': '40.840', 'text': 'equation.'}, {'start': '50.984', 'end': '56.956', 'text': 'To begin we must'}, {'start': '51.451', 'end': '62.028', 'text': 'identify what a line is,'}, {'start': '52.051', 'end': '62.528', 'text': 'therefore the equation will be'}, {'start': '54.320', 'end': '63.062', 'text': 'of first degree.'}, {'start': '57.023', 'end': '67.300', 'text': '>> Daniela Rojas: Yes'}, {'start': '62.095', 'end': '72.005', 'text': '>> Professor Alberto Argon: Is the'}, {'start': '62.595', 'end': '72.005', 'text': 'equation going to be first'}, {'start': '63.129', 'end': '72.005', 'text': 'degree now?  In this type of'}, {'start': '67.367', 'end': '72.005', 'text': 'equations it is very easy.'}, {'start': '73.106', 'end': '79.612', 'text': 'So that it forms Well,'}, {'start': '73.706', 'end': '87.053', 'text': 'we are going to take two points on the'}, {'start': '74.273', 'end': '87.053', 'text': 'line where it intersects exactly.'}, {'start': '79.078', 'end': '87.053', 'text': 'Where you have exact coordinates.'}, {'start': '82.081', 'end': '87.053', 'text': "Yes, let's"}, {'start': '88.188', 'end': '94.227', 'text': 'see what I mean by'}, {'start': '88.688', 'end': '99.165', 'text': 'exact coordinates. Ah, well,'}, {'start': '89.289', 'end': '99.165', 'text': 'I identified that this point will'}, {'start': '89.856', 'end': '99.165', 'text': 'have coordinates.  But eat'}, {'start': '94.293', 'end': '99.165', 'text': 'one, right?'}, {'start': '100.300', 'end': '104.403', 'text': 'Now I identify that this'}, {'start': '100.833', 'end': '109.209', 'text': 'point is going to have coordinates.'}, {'start': '101.367', 'end': '109.209', 'text': 'Well, what coordinates is'}, {'start': '103.369', 'end': '109.209', 'text': "point B going to have? Let's see, tell me."}, {'start': '110.310', 'end': '115.248', 'text': '>> Daniela Rojas: 9'}, {'start': '117.350', 'end': '122.288', 'text': '>> Professor Alberto Argon: 9.9'}, {'start': '125.391', 'end': '132.932', 'text': "And now look what I'm going to"}, {'start': '125.924', 'end': '135.501', 'text': "do. I'm going to draw these lines,"}, {'start': '126.525', 'end': '140.373', 'text': 'the horizontal line and the line.'}, {'start': '132.398', 'end': '140.373', 'text': "and I'm going to count how many units"}, {'start': '132.998', 'end': '140.373', 'text': 'I travel from point a to'}, {'start': '135.568', 'end': '140.373', 'text': "this point. Let's"}, {'start': '141.474', 'end': '156.456', 'text': "see, I'm going to put a period"}, {'start': '142.041', 'end': '156.456', 'text': 'there.  How many units do I travel'}, {'start': '146.912', 'end': '156.456', 'text': 'from point a to this'}, {'start': '151.683', 'end': '156.456', 'text': 'point where?'}, {'start': '160.593', 'end': '170.536', 'text': 'How many places did I travel?'}, {'start': '161.594', 'end': '171.136', 'text': '>> Daniela Rojas: 9'}, {'start': '165.632', 'end': '174.941', 'text': '>> Professor Alberto Argon: down'}, {'start': '167.634', 'end': '179.579', 'text': '>> Daniela Rojas: 9'}, {'start': '170.603', 'end': '179.579', 'text': '>> Professor Alberto Argon: And'}, {'start': '171.203', 'end': '179.579', 'text': 'up.  From this point'}, {'start': '175.008', 'end': '179.579', 'text': 'onwards.'}, {'start': '182.682', 'end': '187.620', 'text': '>> Daniela Rojas: 8'}, {'start': '191.724', 'end': '201.734', 'text': '>> Professor Alberto Argon: Now'}, {'start': '192.291', 'end': '201.734', 'text': 'like that equation we said of'}, {'start': '192.825', 'end': '201.734', 'text': 'first degree.  its shape is going to be'}, {'start': '194.026', 'end': '201.734', 'text': 'this and'}, {'start': '207.840', 'end': '215.782', 'text': "Yes where m.  It's the slope."}, {'start': '217.884', 'end': '225.825', 'text': 'and B is called ordinate ordinate'}, {'start': '226.926', 'end': '237.870', 'text': "at the origin I'm going to"}, {'start': '230.129', 'end': '237.870', 'text': 'compose myself completely.  to the origin'}, {'start': '240.006', 'end': '256.990', 'text': 'and now we must'}, {'start': '240.539', 'end': '256.990', 'text': 'know that it will always be y'}, {'start': '246.979', 'end': '256.990', 'text': 'over x always and what it will be y And'}, {'start': '259.092', 'end': '269.068', 'text': 'x is the horizontal value that we'}, {'start': '259.659', 'end': '269.068', 'text': 'just got.  So'}, {'start': '264.263', 'end': '269.068', 'text': 'how much is the slope of this'}, {'start': '264.830', 'end': '269.068', 'text': 'graph?'}, {'start': '272.171', 'end': '284.784', 'text': '>> Daniela Rojas: it would be 8 out of'}, {'start': '276.308', 'end': '289.155', 'text': '9'}, {'start': '279.178', 'end': '289.155', 'text': '>> Professor Alberto Argon: 8 Ah'}, {'start': '284.250', 'end': '289.155', 'text': 'then if you And now what is B'}, {'start': '291.257', 'end': '296.261', 'text': 'b, it tells me that it is the ordinate at the'}, {'start': '291.857', 'end': '296.828', 'text': 'origin and the ordinate at the origin.  The'}, {'start': '292.458', 'end': '300.332', 'text': "only thing it's telling me is"}, {'start': '293.058', 'end': '300.933', 'text': 'where it intersects the y-axis. The'}, {'start': '296.328', 'end': '305.238', 'text': "only thing it's telling me is the"}, {'start': '296.895', 'end': '305.238', 'text': 'y-intercept.  At what'}, {'start': '300.399', 'end': '305.238', 'text': "point are we cutting the y-axis? Let's"}, {'start': '309.342', 'end': '315.281', 'text': 'see, here is the point a, there it'}, {'start': '309.942', 'end': '315.281', 'text': 'is cutting it.'}, {'start': '310.376', 'end': '315.281', 'text': '>> Daniela Rojas: in'}, {'start': '316.382', 'end': '325.358', 'text': '>> Professor Alberto Argon: No, to the'}, {'start': '316.949', 'end': '330.363', 'text': 'axis.  the Yes the vertical'}, {'start': '319.685', 'end': '330.363', 'text': '>> Daniela Rojas: zero'}, {'start': '323.423', 'end': '330.363', 'text': '>> Professor Alberto Argon: no'}, {'start': '325.425', 'end': '330.363', 'text': '>> Daniela Rojas: in'}, {'start': '333.466', 'end': '336.769', 'text': '>> Professor Alberto Argon: Those'}, {'start': '333.999', 'end': '341.374', 'text': 'coordinates are one then it'}, {'start': '334.533', 'end': '341.374', 'text': 'is cutting the AB axis to the y axis'}, {'start': '335.134', 'end': '341.374', 'text': 'in one.  With this we can now'}, {'start': '336.835', 'end': '341.374', 'text': 'take out.'}, {'start': '343.509', 'end': '364.530', 'text': 'The equation would be and is equal.  to'}, {'start': '347.580', 'end': '364.530', 'text': 'the slope 8 plus one This is'}, {'start': '356.722', 'end': '364.530', 'text': 'the equation of this.  straight'}, {'start': '377.643', 'end': '387.653', 'text': 'Now if you want to see it that'}, {'start': '378.210', 'end': '387.653', 'text': 'way.  What is the'}, {'start': '383.082', 'end': '387.653', 'text': 'x coordinate of this point'}, {'start': '388.754', 'end': '399.699', 'text': '>> Daniela Rojas: zero'}, {'start': '390.756', 'end': '399.699', 'text': '>> Professor Alberto Argon: point'}, {'start': '391.356', 'end': '399.699', 'text': "a So we're going to put zero"}, {'start': '394.794', 'end': '399.699', 'text': 'minus'}, {'start': '403.836', 'end': '414.747', 'text': 'What is the x coordinate of'}, {'start': '404.403', 'end': '414.747', 'text': 'point B'}, {'start': '406.806', 'end': '414.747', 'text': '>> Daniela Rojas: nine'}, {'start': '409.809', 'end': '414.747', 'text': '>> Professor Alberto Argon: 9'}, {'start': '415.848', 'end': '428.861', 'text': "No, it's the other way around, sorry."}, {'start': '418.818', 'end': '428.861', 'text': "It's 9 - 0. And 9 - 0, how much does it"}, {'start': '424.256', 'end': '428.861', 'text': 'give us?'}, {'start': '430.963', 'end': '437.870', 'text': 'These are the x coordinates'}, {'start': '431.530', 'end': '437.870', 'text': 'of the two points now the'}, {'start': '432.030', 'end': '437.870', 'text': 'y coordinates of the two'}, {'start': '433.031', 'end': '437.870', 'text': 'points.'}, {'start': '439.972', 'end': '448.981', 'text': 'We subtract the'}, {'start': '440.505', 'end': '452.985', 'text': 'guide coordinate from this point one.  And it'}, {'start': '443.075', 'end': '452.985', 'text': 'gives us.  this coordinate, the only thing we are'}, {'start': '448.447', 'end': '452.985', 'text': 'going to do is subtract the'}, {'start': '449.048', 'end': '452.985', 'text': 'coordinates in'}, {'start': '455.087', 'end': '465.031', 'text': 'Yes to get those values'}, {'start': '456.088', 'end': '465.031', 'text': '>> Daniela Rojas: 8'}, {'start': '460.126', 'end': '465.031', 'text': '>> Professor Alberto Argon: And these'}, {'start': '460.726', 'end': '465.031', 'text': 'are the ones that go.'}, {'start': '467.166', 'end': '473.005', 'text': 'Up on the slope will go the one with'}, {'start': '467.733', 'end': '476.141', 'text': 'and down will see the one with X eight or'}, {'start': '468.333', 'end': '481.147', 'text': 'nine?  And here the good point will be'}, {'start': '472.538', 'end': '481.147', 'text': 'the x coordinate of the'}, {'start': '473.072', 'end': '481.147', 'text': 'point.  that is cutting.  to the'}, {'start': '476.208', 'end': '481.147', 'text': 'axis that'}, {'start': '483.249', 'end': '488.187', 'text': 'is in and sorry that is one and'}, {'start': '483.816', 'end': '488.187', 'text': 'our equation is done.'}, {'start': '491.290', 'end': '504.337', 'text': "Now what we can do if we don't"}, {'start': '491.890', 'end': '504.337', 'text': 'want it in fraction.  It is to'}, {'start': '496.362', 'end': '504.337', 'text': 'multiply everything.  That is,'}, {'start': '499.532', 'end': '504.337', 'text': 'by the denominator.'}, {'start': '506.439', 'end': '514.380', 'text': 'And how much is nine times and 9'}, {'start': '509.508', 'end': '514.380', 'text': '>> Daniela Rojas: 9'}, {'start': '515.481', 'end': '520.419', 'text': '>> Professor Alberto Argon: And how much'}, {'start': '516.081', 'end': '520.419', 'text': 'is nine times eight ninths?'}, {'start': '521.520', 'end': '534.567', 'text': '>> Daniela Rojas: 72 ninths'}, {'start': '525.558', 'end': '535.167', 'text': '>> Professor Alberto Argon: And what'}, {'start': '526.158', 'end': '537.536', 'text': 'is 72 divided by 9?'}, {'start': '529.595', 'end': '538.537', 'text': '>> Daniela Rojas: 8'}, {'start': '534.634', 'end': '543.543', 'text': '>> Professor Alberto Argon: 8 x + 9'}, {'start': '535.268', 'end': '543.543', 'text': '* 1'}, {'start': '537.603', 'end': '543.543', 'text': '>> Daniela Rojas: 9'}, {'start': '538.604', 'end': '543.543', 'text': '>> Professor Alberto Argon: 9'}, {'start': '545.645', 'end': '553.586', 'text': 'Without fractions and now the only thing we are'}, {'start': '546.245', 'end': '553.586', 'text': 'going to do is pass the'}, {'start': '546.812', 'end': '553.586', 'text': 'eight.  x on the other side'}, {'start': '554.687', 'end': '564.697', 'text': '>> Daniela Rojas: subtracting'}, {'start': '559.725', 'end': '564.697', 'text': '>> teacher Alberto Argon: yes'}, {'start': '560.225', 'end': '564.697', 'text': 'So it would be minus eight x plus'}, {'start': '560.826', 'end': '564.697', 'text': 'nine and'}, {'start': '565.798', 'end': '574.707', 'text': 'It is equal to 9 and this is the'}, {'start': '566.298', 'end': '574.707', 'text': 'equation of this line.  Could'}, {'start': '569.902', 'end': '574.707', 'text': 'be.   It'}, {'start': '575.808', 'end': '580.746', 'text': 'all depends on what they'}, {'start': '576.408', 'end': '580.746', 'text': 'ask for, this is what it is called.'}, {'start': '582.848', 'end': '593.793', 'text': 'slope ordinate at the origin and'}, {'start': '583.415', 'end': '593.793', 'text': 'equal to eight ninths of X plus'}, {'start': '585.951', 'end': '593.793', 'text': 'one is called slope ordinate'}, {'start': '586.551', 'end': '593.793', 'text': 'at the origin and that'}, {'start': '594.894', 'end': '599.865', 'text': 'is, equal to it It'}, {'start': '601.967', 'end': '606.872', 'text': 'is equal to zero That is the'}, {'start': '602.467', 'end': '606.872', 'text': 'general one.   You'}, {'start': '614.013', 'end': '622.955', 'text': 'more or less understood.'}, {'start': '617.016', 'end': '622.955', 'text': '>> Daniela Rojas: Yes'}, {'start': '618.017', 'end': '622.955', 'text': '>> Professor Alberto Argon: I say.'}, {'start': '625.057', 'end': '630.029', 'text': 'If you more or less understood it,'}, {'start': '625.624', 'end': '630.029', 'text': "let's put another one to see."}, {'start': '632.131', 'end': '637.036', 'text': 'allow me, let me'}, {'start': '666.298', 'end': '677.209', 'text': ">> Daniela Rojas: I'm going"}, {'start': '670.336', 'end': '677.209', 'text': '>> Professor Alberto Argon: when'}, {'start': '670.903', 'end': '677.209', 'text': 'you finish'}, {'start': '672.304', 'end': '677.209', 'text': '>> Daniela Rojas: yes'}, {'start': '778.911', 'end': '783.849', 'text': 'ready'}, {'start': '813.178', 'end': '823.122', 'text': ">> Professor Alberto Argon: Let's see,"}, {'start': '813.745', 'end': '823.122', 'text': 'there are both of them.  points on the'}, {'start': '818.417', 'end': '823.122', 'text': 'line, tell me the coordinates of'}, {'start': '818.984', 'end': '823.122', 'text': 'each point from point a'}, {'start': '826.292', 'end': '833.265', 'text': '>> Daniela Rojas: Start with x,'}, {'start': '826.892', 'end': '837.269', 'text': 'right?'}, {'start': '829.295', 'end': '840.272', 'text': '>> Professor Alberto Argon: Yes, you'}, {'start': '829.828', 'end': '845.277', 'text': 'always start with x.'}, {'start': '833.332', 'end': '845.844', 'text': '>> Daniela Rojas: Minus three.'}, {'start': '837.336', 'end': '846.411', 'text': '>> Teacher Alberto Argon: comma'}, {'start': '840.339', 'end': '850.282', 'text': '>> Daniela Rojas: nine'}, {'start': '845.344', 'end': '850.282', 'text': '>> Teacher Alberto Argon: nine'}, {'start': '845.911', 'end': '850.282', 'text': 'Now tell me the coordinates of'}, {'start': '846.478', 'end': '850.282', 'text': 'point B'}, {'start': '853.419', 'end': '858.357', 'text': '>> Daniela Rojas: seven point'}, {'start': '853.952', 'end': '858.357', 'text': 'three'}, {'start': '863.495', 'end': '872.404', 'text': '>> Teacher Alberto Argon: now'}, {'start': '867.499', 'end': '872.404', 'text': 'draw a horizontal line'}, {'start': '875.541', 'end': '881.246', 'text': 'in such a way that it reaches'}, {'start': '876.108', 'end': '885.484', 'text': 'where point B is now a'}, {'start': '876.708', 'end': '885.484', 'text': "vertical line.  Yes, it doesn't"}, {'start': '880.712', 'end': '885.484', 'text': 'matter, if I draw it below or'}, {'start': '881.313', 'end': '885.484', 'text': "above it doesn't matter."}, {'start': '887.586', 'end': '892.757', 'text': "Now let's subtract them."}, {'start': '888.587', 'end': '899.631', 'text': '>> Daniela Rojas: Yes'}, {'start': '891.623', 'end': '902.634', 'text': '>> Professor Alberto Argon: We can'}, {'start': '892.223', 'end': '907.606', 'text': 'write minus three minus seven.'}, {'start': '895.560', 'end': '907.606', 'text': 'And how much would that give us?'}, {'start': '899.698', 'end': '907.606', 'text': '>> Daniela Rojas: four'}, {'start': '902.701', 'end': '907.606', 'text': '>> Professor Alberto Argon: no'}, {'start': '912.745', 'end': '919.317', 'text': '>> Daniela Rojas: ten'}, {'start': '917.783', 'end': '922.754', 'text': '>> Professor Alberto Argon:'}, {'start': '918.250', 'end': '923.254', 'text': 'Remember if'}, {'start': '918.784', 'end': '927.759', 'text': 'the numbers that were made have the same sign.'}, {'start': '922.821', 'end': '932.798', 'text': '>> Daniela Rojas: Well, yes,'}, {'start': '923.321', 'end': '935.834', 'text': 'we have'}, {'start': '927.826', 'end': '936.401', 'text': '>> Professor Alberto Argon: Then'}, {'start': '928.426', 'end': '940.773', 'text': 'how much'}, {'start': '932.865', 'end': '940.773', 'text': '>> Daniela Rojas: No'}, {'start': '935.901', 'end': '940.773', 'text': '>> Professor Alberto Argon: Give no'}, {'start': '936.468', 'end': '940.773', 'text': 'less.'}, {'start': '941.874', 'end': '949.848', 'text': "And we're going to count it. Look, in"}, {'start': '942.407', 'end': '949.848', 'text': 'squares, one two three four five six seven'}, {'start': '942.975', 'end': '949.848', 'text': 'eight nine.'}, {'start': '952.985', 'end': '961.927', 'text': 'Now here we are going to do the'}, {'start': '953.518', 'end': '961.927', 'text': 'same thing, we are going to subtract them.'}, {'start': '957.022', 'end': '961.927', 'text': 'We subtract nine.'}, {'start': '969.068', 'end': '978.610', 'text': "6 and let's see if it's true."}, {'start': '974.039', 'end': '979.111', 'text': 'Yes'}, {'start': '977.109', 'end': '983.048', 'text': '>> Daniela Rojas: 6'}, {'start': '978.110', 'end': '983.048', 'text': '>> Professor Alberto Argon: That'}, {'start': '978.677', 'end': '983.048', 'text': 'will help me to get the'}, {'start': '979.177', 'end': '983.048', 'text': 'slope, we said.'}, {'start': '987.152', 'end': '997.096', 'text': 'So the slope is going to be'}, {'start': '987.719', 'end': '997.096', 'text': 'equal to and over.  how much is Y worth'}, {'start': '1003.235', 'end': '1008.173', 'text': '>> Daniela Rojas: the value'}, {'start': '1013.278', 'end': '1018.750', 'text': '>> Professor Alberto Argon: No, no,'}, {'start': '1013.878', 'end': '1022.721', 'text': 'no, here of these two or well'}, {'start': '1014.445', 'end': '1027.292', 'text': 'Which is the vertical and which is the'}, {'start': '1018.216', 'end': '1027.292', 'text': 'horizontal and is the vertical x is'}, {'start': '1018.816', 'end': '1027.292', 'text': 'the Of these two that we just took'}, {'start': '1022.788', 'end': '1027.292', 'text': 'out.'}, {'start': '1028.393', 'end': '1033.332', 'text': '>> Daniela Rojas: The horizontal'}, {'start': '1028.993', 'end': '1033.332', 'text': 'is seven.'}, {'start': '1034.433', 'end': '1039.905', 'text': '>> Professor Alberto Argon: No, no,'}, {'start': '1035.033', 'end': '1040.472', 'text': "let's see, we already did the math, my"}, {'start': '1035.600', 'end': '1042.607', 'text': 'friend. I mean, I put them in to'}, {'start': '1039.438', 'end': '1044.376', 'text': "get the numbers, but I'm"}, {'start': '1039.971', 'end': '1044.976', 'text': 'interested in these two. Which one is the'}, {'start': '1040.539', 'end': '1049.381', 'text': 'vertical one and which ones are the'}, {'start': '1042.674', 'end': '1049.381', 'text': 'horizontal ones?'}, {'start': '1044.443', 'end': '1049.381', 'text': '>> Daniela Rojas: The horizontal'}, {'start': '1045.043', 'end': '1049.381', 'text': 'is minus ten, right?'}, {'start': '1051.483', 'end': '1056.187', 'text': '>> Professor Alberto Argon: It is this'}, {'start': '1052.083', 'end': '1060.459', 'text': 'in x then remember that X is'}, {'start': '1052.684', 'end': '1060.459', 'text': 'the horizontal.  and y is the'}, {'start': '1055.653', 'end': '1060.459', 'text': 'vertical So how much are y worth'}, {'start': '1062.561', 'end': '1070.502', 'text': 'In x.'}, {'start': '1065.597', 'end': '1070.502', 'text': '>> Daniela Rojas: minus 10'}, {'start': '1071.603', 'end': '1076.508', 'text': '>> Professor Alberto Argon: Now'}, {'start': '1072.170', 'end': '1076.508', 'text': 'how much is more divided by less.'}, {'start': '1077.609', 'end': '1084.316', 'text': '>> Daniela Rojas: less'}, {'start': '1082.681', 'end': '1088.886', 'text': '>> Professor Alberto Argon: And the'}, {'start': '1083.214', 'end': '1089.420', 'text': 'sign must go to the center, it'}, {'start': '1083.782', 'end': '1089.954', 'text': 'must not go above or below, it must'}, {'start': '1084.382', 'end': '1093.758', 'text': 'go to the center.  We already have the'}, {'start': '1088.953', 'end': '1098.730', 'text': 'slope minus six tenths'}, {'start': '1089.487', 'end': '1098.730', 'text': 'now minus six tenths, it'}, {'start': '1090.021', 'end': '1098.730', 'text': 'can be simplified.  How much'}, {'start': '1093.825', 'end': '1098.730', 'text': 'would it be?'}, {'start': '1099.831', 'end': '1104.736', 'text': '>> Daniela Rojas: three-fifths'}, {'start': '1105.837', 'end': '1119.818', 'text': '>> Professor Alberto Argon:'}, {'start': '1106.337', 'end': '1119.818', 'text': 'We already have the pending one.'}, {'start': '1110.909', 'end': '1119.818', 'text': 'We can now take out.  A b.'}, {'start': '1120.919', 'end': '1132.898', 'text': 'But it turns out that the point'}, {'start': '1121.486', 'end': '1132.898', 'text': "where we cut b.  Well, it's not"}, {'start': '1123.087', 'end': '1132.898', 'text': 'exactly true.  It is not exact.'}, {'start': '1133.999', 'end': '1138.904', 'text': "So what are we going to do I'm"}, {'start': '1140.005', 'end': '1147.980', 'text': 'going to show you this'}, {'start': '1151.083', 'end': '1161.159', 'text': "When we don't have the"}, {'start': '1151.650', 'end': '1166.064', 'text': 'exact value where we cut b.'}, {'start': '1156.054', 'end': '1166.064', 'text': 'What is going to be done is to take out.'}, {'start': '1160.058', 'end': '1166.064', 'text': 'the equation in this way'}, {'start': '1161.225', 'end': '1166.064', 'text': 'tells us.'}, {'start': '1169.201', 'end': '1180.145', 'text': '10 2 a Sorry, let me agree.'}, {'start': '1175.140', 'end': '1180.145', 'text': "Not to invent Let's see, let me."}, {'start': '1181.246', 'end': '1186.185', 'text': 'my'}, {'start': '1188.287', 'end': '1205.270', 'text': "Minus one.  It's the same.  To m.  by"}, {'start': '1200.431', 'end': '1205.270', 'text': 'x minus x 1'}, {'start': '1219.451', 'end': '1232.464', 'text': "And now let's see what it is.  They are"}, {'start': '1224.589', 'end': '1232.464', 'text': 'the coordinates of any'}, {'start': '1225.190', 'end': '1232.464', 'text': 'two points.  If I want'}, {'start': '1227.726', 'end': '1232.464', 'text': 'this to be it.   I'}, {'start': '1236.568', 'end': '1241.473', 'text': 'can say that this is'}, {'start': '1237.135', 'end': '1241.473', 'text': 'x1 and this is y1.'}, {'start': '1242.574', 'end': '1250.515', 'text': 'But I can say that x one has'}, {'start': '1243.174', 'end': '1250.515', 'text': 'some that are these, that is, I can'}, {'start': '1243.775', 'end': '1250.515', 'text': 'grab the point that I want.'}, {'start': '1245.543', 'end': '1250.515', 'text': 'Yes'}, {'start': '1257.689', 'end': '1267.232', 'text': 'If you already understood that.'}, {'start': '1261.727', 'end': '1267.833', 'text': ">> Daniela Rojas: It's one of the"}, {'start': '1262.327', 'end': '1273.739', 'text': 'two coordinates, right?'}, {'start': '1266.732', 'end': '1278.677', 'text': '>> Professor Alberto Argon: Yes, the one'}, {'start': '1267.299', 'end': '1278.677', 'text': 'you want, it can be a'}, {'start': '1267.899', 'end': '1278.677', 'text': 'or B. So how much are you'}, {'start': '1273.805', 'end': '1278.677', 'text': 'going to take?'}, {'start': '1279.778', 'end': '1286.785', 'text': '>> Daniela Rojas: Go'}, {'start': '1282.781', 'end': '1287.385', 'text': '>> Professor Alberto Argon: or b.'}, {'start': '1283.314', 'end': '1291.757', 'text': 'So how much is it worth? And one would be'}, {'start': '1283.915', 'end': '1291.757', 'text': 'and'}, {'start': '1286.852', 'end': '1291.757', 'text': '>> Daniela Rojas: Without minus three'}, {'start': '1293.892', 'end': '1301.800', 'text': '>> Professor Alberto Argon: It is equal'}, {'start': '1294.492', 'end': '1301.800', 'text': 'to the slope.  three-fifths'}, {'start': '1306.905', 'end': '1311.843', 'text': '>> Daniela Rojas: Minus seven.'}, {'start': '1314.980', 'end': '1323.554', 'text': '>> Professor Alberto Argon: And now'}, {'start': '1315.580', 'end': '1325.957', 'text': 'the 5th is doing.'}, {'start': '1319.985', 'end': '1326.557', 'text': '>> Daniela Rojas: dividing'}, {'start': '1323.021', 'end': '1328.993', 'text': '>> Professor Alberto Argon: How'}, {'start': '1323.621', 'end': '1329.527', 'text': 'did we do?'}, {'start': '1326.024', 'end': '1337.068', 'text': '>> Daniela Rojas: multiplying'}, {'start': '1329.060', 'end': '1347.712', 'text': '>> Professor Alberto Argon: We would have'}, {'start': '1329.593', 'end': '1348.312', 'text': "5. times and minus 3 It's the"}, {'start': '1337.135', 'end': '1349.447', 'text': 'same.  by x minus seven And'}, {'start': '1347.178', 'end': '1353.118', 'text': 'we apply distributive property'}, {'start': '1347.779', 'end': '1358.123', 'text': 'on both sides, that is, the number'}, {'start': '1348.379', 'end': '1363.128', 'text': 'on the outside multiplies the two on the'}, {'start': '1349.514', 'end': '1363.128', 'text': 'inside.'}, {'start': '1353.185', 'end': '1363.128', 'text': '>> Daniela Rojas: 5'}, {'start': '1358.190', 'end': '1363.128', 'text': '>> Professor Alberto Argon: five'}, {'start': '1366.231', 'end': '1380.178', 'text': '>> Daniela Rojas: minus 15'}, {'start': '1370.268', 'end': '1380.178', 'text': ">> Professor Alberto Argon: It's the"}, {'start': '1370.768', 'end': '1380.178', 'text': 'same.'}, {'start': '1375.240', 'end': '1380.178', 'text': '>> Daniela Rojas: minus 3x'}, {'start': '1381.279', 'end': '1392.257', 'text': '>> Professor Alberto Argon: minus 3x'}, {'start': '1384.215', 'end': '1392.257', 'text': 'then'}, {'start': '1387.352', 'end': '1392.257', 'text': '>> Daniela Rojas: Well plus 21'}, {'start': '1401.433', 'end': '1408.340', 'text': '>> Professor Alberto Argon: And now'}, {'start': '1402.033', 'end': '1408.340', 'text': 'what I want to know is'}, {'start': '1402.567', 'end': '1408.340', 'text': 'how much it is worth, the point where it is'}, {'start': '1403.168', 'end': '1408.340', 'text': 'cutting.  here'}, {'start': '1411.443', 'end': '1420.418', 'text': "to the axis and I'm going to do the"}, {'start': '1411.910', 'end': '1420.952', 'text': "following, I'm going to clear and"}, {'start': '1414.512', 'end': '1427.459', 'text': 'minus fifteen How does it happen'}, {'start': '1416.481', 'end': '1427.459', 'text': '>> Daniela Rojas: adding'}, {'start': '1420.485', 'end': '1427.459', 'text': '>> teacher Alberto Argon: it would be'}, {'start': '1421.018', 'end': '1427.459', 'text': "five and It's equal."}, {'start': '1434.599', 'end': '1447.111', 'text': 'and we would have five left and it is equal'}, {'start': '1435.199', 'end': '1448.580', 'text': "to minus 3 That's that sum."}, {'start': '1444.609', 'end': '1449.581', 'text': '>> Daniela Rojas: 36'}, {'start': '1446.611', 'end': '1450.148', 'text': '>> Professor Alberto Argon: 21 more'}, {'start': '1448.647', 'end': '1454.553', 'text': '>> Daniela Rojas: 36'}, {'start': '1449.648', 'end': '1454.553', 'text': '>> Professor Alberto Argon: 15 more'}, {'start': '1456.721', 'end': '1465.497', 'text': '>> Daniela Rojas: dividing'}, {'start': '1459.724', 'end': '1466.097', 'text': '>> Professor Alberto Argon:'}, {'start': '1460.191', 'end': '1469.668', 'text': "dividing I'm going to continue"}, {'start': '1465.096', 'end': '1469.668', 'text': 'here, okay?  In order not to make it'}, {'start': '1465.563', 'end': '1469.668', 'text': 'small, then it would be the'}, {'start': '1466.164', 'end': '1469.668', 'text': 'same for us.'}, {'start': '1471.770', 'end': '1482.714', 'text': 'At least 3x +?  36 between 5'}, {'start': '1484.816', 'end': '1489.754', 'text': 'and now this 5'}, {'start': '1490.855', 'end': '1493.057', 'text': 'is going to divide the two, because'}, {'start': '1491.422', 'end': '1494.225', 'text': 'that was what they told us in'}, {'start': '1491.956', 'end': '1501.967', 'text': 'fractions, that when above we'}, {'start': '1492.523', 'end': '1506.871', 'text': 'have two terms and below one'}, {'start': '1493.124', 'end': '1510.909', 'text': 'can be separated then This is'}, {'start': '1494.292', 'end': '1511.443', 'text': 'going to be.  Minus three.  of X'}, {'start': '1502.033', 'end': '1515.914', 'text': 'plus 36 divided by 5'}, {'start': '1506.938', 'end': '1515.914', 'text': '>> Daniela Rojas: Yes'}, {'start': '1510.976', 'end': '1515.914', 'text': '>> Professor Alberto Argon: Yes and'}, {'start': '1511.509', 'end': '1515.914', 'text': 'now tell me how much is 36.'}, {'start': '1530.095', 'end': '1540.038', 'text': '>> Daniela Rojas: 7.2'}, {'start': '1535.133', 'end': '1540.038', 'text': '>> Professor Alberto Argon: It is the'}, {'start': '1535.700', 'end': '1540.038', 'text': 'value of this point where'}, {'start': '1543.141', 'end': '1548.079', 'text': 'Because remember This is the'}, {'start': '1543.641', 'end': '1548.079', 'text': 'ordinate at the origin, that is, it is'}, {'start': '1544.208', 'end': '1548.079', 'text': 'where it intersects the axis.'}, {'start': '1550.181', 'end': '1555.686', 'text': "And yes, I say I know that maybe it's"}, {'start': '1550.781', 'end': '1556.287', 'text': 'costing you work.'}, {'start': '1551.282', 'end': '1556.754', 'text': '>> Daniela Rojas: Yes'}, {'start': '1555.186', 'end': '1557.321', 'text': '>> Professor Alberto Argon: Because you'}, {'start': '1555.753', 'end': '1562.160', 'text': "hadn't seen it, but it's the"}, {'start': '1556.353', 'end': '1562.160', 'text': 'same as everything else, based on'}, {'start': '1556.821', 'end': '1562.160', 'text': "practice. You're going to have to"}, {'start': '1557.421', 'end': '1562.160', 'text': 'record it.'}, {'start': '1565.296', 'end': '1570.201', 'text': 'Copy it.'}, {'start': '1573.271', 'end': '1578.375', 'text': "And I don't know if there's anything you didn't"}, {'start': '1573.838', 'end': '1583.214', 'text': "know how to do, or something that's"}, {'start': '1574.405', 'end': '1583.214', 'text': 'new to you.  Maybe something'}, {'start': '1575.539', 'end': '1583.214', 'text': "new for you.  It's this"}, {'start': '1578.442', 'end': '1583.214', 'text': 'equation.'}, {'start': '1584.349', 'end': '1589.254', 'text': "It's this equation but in"}, {'start': '1584.816', 'end': '1589.254', 'text': "reality.   It's"}, {'start': '1590.388', 'end': '1595.327', 'text': 'just a matter of changing data and'}, {'start': '1590.921', 'end': '1595.327', 'text': 'doing the math. You'}, {'start': '1591.522', 'end': '1595.327', 'text': 'know how to do the math.'}, {'start': '1598.430', 'end': '1606.338', 'text': "Yes, copy copy and we'll"}, {'start': '1598.930', 'end': '1606.338', 'text': 'put another one right now.'}, {'start': '1601.466', 'end': '1606.338', 'text': '>> Daniela Rojas: Yes,'}, {'start': '1790.421', 'end': '1803.401', 'text': 'ready'}, {'start': '1795.460', 'end': '1803.401', 'text': ">> Professor Alberto Argon: Let's see,"}, {'start': '1796.027', 'end': '1803.401', 'text': "let's put another one.  Let's"}, {'start': '1798.596', 'end': '1803.401', 'text': 'put this'}, {'start': '1822.587', 'end': '1827.525', 'text': "There it is, we're going to get the"}, {'start': '1823.120', 'end': '1827.525', 'text': 'coordinates of points a and b.'}, {'start': '1831.629', 'end': '1838.536', 'text': 'Oh no sorry, It was the same but it'}, {'start': '1832.229', 'end': '1838.536', 'text': "didn't copy the other one.  Let me"}, {'start': '1874.806', 'end': '1879.744', 'text': 'There it is.'}, {'start': '1891.923', 'end': '1898.896', 'text': '>> Daniela Rojas: It would be less.'}, {'start': '1896.961', 'end': '1906.871', 'text': '>> Teacher Alberto Argon: minus 3'}, {'start': '1898.963', 'end': '1906.871', 'text': '>> Daniela Rojas: like'}, {'start': '1901.966', 'end': '1906.871', 'text': '>> Teacher Alberto Argon: ,'}, {'start': '1908.973', 'end': '1913.945', 'text': '>> Daniela Rojas: three six point'}, {'start': '1909.573', 'end': '1913.945', 'text': 'nine'}, {'start': '1919.083', 'end': '1921.285', 'text': '>> Teacher Alberto Argon: So I'}, {'start': '1919.683', 'end': '1929.027', 'text': 'told you to draw'}, {'start': '1920.084', 'end': '1929.027', 'text': "horizontal or vertical lines, it doesn't"}, {'start': '1920.617', 'end': '1929.027', 'text': 'matter if above or below'}, {'start': '1924.021', 'end': '1929.027', 'text': 'all of them.'}, {'start': '1931.129', 'end': '1939.037', 'text': 'So in order not to have to count'}, {'start': '1931.729', 'end': '1939.037', 'text': 'the squares, we are going to do the'}, {'start': '1932.296', 'end': '1939.037', 'text': 'subtraction. The subtraction would be It'}, {'start': '1941.172', 'end': '1946.110', 'text': 'is not six less.'}, {'start': '1954.252', 'end': '1965.196', 'text': 'And less for less, how much do they'}, {'start': '1954.819', 'end': '1965.196', 'text': 'give us?'}, {'start': '1957.288', 'end': '1965.196', 'text': '>> Daniela Rojas: more'}, {'start': '1960.291', 'end': '1965.196', 'text': '>> Professor Alberto Argon: well'}, {'start': '1972.303', 'end': '1977.308', 'text': 'And we are going to count squares and'}, {'start': '1972.836', 'end': '1977.875', 'text': 'so on to see if one'}, {'start': '1973.437', 'end': '1978.476', 'text': 'two three four is true.'}, {'start': '1973.837', 'end': '1979.043', 'text': '>> Daniela Rojas: 9'}, {'start': '1977.375', 'end': '1980.845', 'text': '>> Professor Alberto Argon: five,'}, {'start': '1977.942', 'end': '1986.350', 'text': "six seven eight nine, that's"}, {'start': '1978.542', 'end': '1991.389', 'text': "good. Let's see, let's do it here."}, {'start': '1980.311', 'end': '1996.394', 'text': 'We will always'}, {'start': '1980.911', 'end': '1996.994', 'text': 'subtract the smallest from the largest.  nine'}, {'start': '1986.417', 'end': '2001.432', 'text': 'less And this is'}, {'start': '1991.456', 'end': '2001.432', 'text': '>> Daniela Rojas: 6'}, {'start': '1996.461', 'end': '2001.432', 'text': ">> Professor Alberto Argon: And let's"}, {'start': '1997.061', 'end': '2001.432', 'text': "see if it's true."}, {'start': '2003.534', 'end': '2012.477', 'text': 'Then we can get the'}, {'start': '2004.067', 'end': '2012.477', 'text': 'slope.  It would be the horizontal one.'}, {'start': '2013.578', 'end': '2027.558', 'text': '>> Daniela Rojas: 9 out of 6'}, {'start': '2017.615', 'end': '2027.558', 'text': '>> Professor Alberto Argon: No,'}, {'start': '2018.148', 'end': '2027.558', 'text': 'sorry, the vertical one out of the'}, {'start': '2018.682', 'end': '2027.558', 'text': 'horizontal one.  6 out of 9'}, {'start': '2028.659', 'end': '2036.601', 'text': 'Is it always the vertical between the'}, {'start': '2029.259', 'end': '2036.601', 'text': "horizontal always?  That's the"}, {'start': '2031.828', 'end': '2036.601', 'text': 'slope.'}, {'start': '2039.670', 'end': '2046.644', 'text': "We're still going to figure out where"}, {'start': '2040.270', 'end': '2046.644', 'text': 'B cuts, but I say, here it'}, {'start': '2040.804', 'end': '2046.644', 'text': "looks like five.  But it's"}, {'start': '2047.745', 'end': '2054.685', 'text': 'better to get it the other'}, {'start': '2048.345', 'end': '2054.685', 'text': "way, because we're going to grab"}, {'start': '2048.879', 'end': '2054.685', 'text': 'any point, which point do you'}, {'start': '2049.946', 'end': '2054.685', 'text': 'want to grab a or b?'}, {'start': '2059.824', 'end': '2068.766', 'text': 'and the'}, {'start': '2063.828', 'end': '2068.766', 'text': '>> Daniela Rojas: 9'}, {'start': '2069.901', 'end': '2082.814', 'text': '>> Professor Alberto Argon: And now'}, {'start': '2070.501', 'end': '2082.814', 'text': 'the equation we said it was.  and'}, {'start': '2073.904', 'end': '2082.814', 'text': 'minus and One equals m.'}, {'start': '2083.915', 'end': '2088.853', 'text': 'for x less'}, {'start': '2095.993', 'end': '2100.932', 'text': 'We changed the data.'}, {'start': '2111.042', 'end': '2120.050', 'text': ">> Daniela Rojas: Well, I'm not"}, {'start': '2111.609', 'end': '2125.022', 'text': 'worth 9'}, {'start': '2116.080', 'end': '2125.022', 'text': '>> Professor Alberto Argon: How much is'}, {'start': '2116.647', 'end': '2125.022', 'text': 'the slope worth?'}, {'start': '2120.117', 'end': '2125.022', 'text': '>> Daniela Rojas: 6 out of 9'}, {'start': '2129.160', 'end': '2137.135', 'text': '>> Professor Alberto Argon: And this'}, {'start': '2129.727', 'end': '2137.135', 'text': 'is going to be for x, how much is x 1 worth?'}, {'start': '2132.163', 'end': '2137.135', 'text': '>> Daniela Rojas: 6'}, {'start': '2138.236', 'end': '2141.505', 'text': '>> Professor Alberto Argon: and now'}, {'start': '2138.769', 'end': '2148.146', 'text': 'we have everything, just do'}, {'start': '2139.337', 'end': '2148.146', 'text': 'the math and well the'}, {'start': '2139.871', 'end': '2148.146', 'text': 'nine that is dividing happens.'}, {'start': '2143.140', 'end': '2148.146', 'text': 'multiplying It'}, {'start': '2150.248', 'end': '2158.189', 'text': 'is equal to 6. by'}, {'start': '2159.290', 'end': '2171.302', 'text': 'How would it be without parentheses'}, {'start': '2163.327', 'end': '2171.302', 'text': '>> Daniela Rojas: 9 and minus 81'}, {'start': '2175.373', 'end': '2180.311', 'text': 'It is equal to 6x.'}, {'start': '2184.448', 'end': '2194.392', 'text': '>> Professor Alberto Argon: And'}, {'start': '2184.948', 'end': '2194.392', 'text': 'we pass the 81 to the other side, that'}, {'start': '2185.515', 'end': '2194.392', 'text': 'is, we are going to clear there.  9 and'}, {'start': '2205.569', 'end': '2210.474', 'text': 'And we make that count nine.'}, {'start': '2213.577', 'end': '2222.520', 'text': '6x And how much does it give us plus or minus 36'}, {'start': '2218.082', 'end': '2222.520', 'text': '+ 81'}, {'start': '2242.740', 'end': '2252.683', 'text': '>> Daniela Rojas: minus 36 + 81'}, {'start': '2247.678', 'end': '2252.683', 'text': '45 45'}, {'start': '2254.785', 'end': '2259.724', 'text': '>> Professor Alberto Argon: I'}, {'start': '2255.385', 'end': '2259.724', 'text': "'m also going to move this for you."}, {'start': '2261.826', 'end': '2269.767', 'text': 'plus 45 and move the 9 that is'}, {'start': '2262.359', 'end': '2269.767', 'text': 'multiplying to the other side'}, {'start': '2262.860', 'end': '2269.767', 'text': 'dividing It would be and is equal to'}, {'start': '2272.870', 'end': '2281.812', 'text': '+ 45 between 9 How much is 45.'}, {'start': '2285.950', 'end': '2295.893', 'text': 'What would it be?  Plus five Ah'}, {'start': '2291.321', 'end': '2295.893', 'text': 'means yes.'}, {'start': '2303.134', 'end': '2308.039', 'text': 'yes'}, {'start': '2400.698', 'end': '2407.904', 'text': '>> Daniela Rojas: ready'}, {'start': '2405.703', 'end': '2416.647', 'text': '>> teacher Alberto Argon: Well,'}, {'start': '2406.270', 'end': '2422.052', 'text': 'this equation or this form of'}, {'start': '2406.837', 'end': '2422.652', 'text': 'equation.  Its name is called'}, {'start': '2407.971', 'end': '2426.256', 'text': 'point slope point'}, {'start': '2416.714', 'end': '2426.857', 'text': 'slope Why is it called that?'}, {'start': '2422.118', 'end': '2430.761', 'text': 'Well, because they give us a point'}, {'start': '2422.719', 'end': '2431.295', 'text': 'and they give us a slope and that is the'}, {'start': '2426.323', 'end': '2433.764', 'text': 'way in which this'}, {'start': '2426.924', 'end': '2434.364', 'text': 'point slope equation is obtained.'}, {'start': '2430.828', 'end': '2443.807', 'text': ">> Daniela Rojas: What's the"}, {'start': '2431.361', 'end': '2444.374', 'text': 'point?'}, {'start': '2433.831', 'end': '2447.878', 'text': '>> Professor Alberto Argon: to the point'}, {'start': '2438.802', 'end': '2448.478', 'text': 'And the slope six ninths.'}, {'start': '2443.874', 'end': '2449.079', 'text': '>> Daniela Rojas: And that time'}, {'start': '2444.441', 'end': '2453.217', 'text': 'where did it come from?'}, {'start': '2447.945', 'end': '2457.921', 'text': '>> Professor Alberto Argon: Ah, well, it'}, {'start': '2448.545', 'end': '2458.521', 'text': "wasn't the point we took from"}, {'start': '2449.146', 'end': '2462.927', 'text': "here.  And we don't calculate the slope"}, {'start': '2453.283', 'end': '2462.927', 'text': 'here.'}, {'start': '2457.988', 'end': '2462.927', 'text': '>> Daniela Rojas: Ah yes ...'}, {'start': '2464.028', 'end': '2468.933', 'text': ">> Professor Alberto Argon: I mean, we didn't"}, {'start': '2464.628', 'end': '2468.933', 'text': "get her out of here, she didn't leave"}, {'start': '2465.229', 'end': '2468.933', 'text': 'here and the nine.   I did'}, {'start': '2471.068', 'end': '2476.974', 'text': "n't invent any data,"}, {'start': '2471.568', 'end': '2481.979', 'text': "we're not inventing it, we're"}, {'start': '2472.069', 'end': '2481.979', 'text': 'using what our graph gives us'}, {'start': '2474.171', 'end': '2481.979', 'text': '.'}, {'start': '2477.041', 'end': '2481.979', 'text': '>> Daniela Rojas: yes,'}, {'start': '2534.365', 'end': '2539.270', 'text': 'ready'}, {'start': '2541.372', 'end': '2549.346', 'text': '>> Professor Alberto Argon: look'}, {'start': '2544.408', 'end': '2549.346', 'text': 'so that'}, {'start': '2550.447', 'end': '2555.386', 'text': 'when our'}, {'start': '2556.487', 'end': '2564.428', 'text': 'straight line is of this type, that is,'}, {'start': '2557.054', 'end': '2564.428', 'text': 'has this shape, it goes'}, {'start': '2557.588', 'end': '2564.428', 'text': 'up.  on the left side is'}, {'start': '2559.890', 'end': '2564.428', 'text': 'down.   It'}, {'start': '2565.529', 'end': '2570.467', 'text': 'is said that the slope?'}, {'start': '2574.538', 'end': '2583.880', 'text': 'And when it has this shape.'}, {'start': '2579.642', 'end': '2593.557', 'text': 'Now let the left side be'}, {'start': '2580.176', 'end': '2593.557', 'text': 'up and the right side be'}, {'start': '2580.743', 'end': '2593.557', 'text': 'down.  Then the slope.   It'}, {'start': '2586.550', 'end': '2593.557', 'text': 'is negative.  Yes'}, {'start': '2597.695', 'end': '2606.637', 'text': '>> Daniela Rojas: Yes'}, {'start': '2601.732', 'end': '2606.637', 'text': '>> Professor Alberto Argon: And'}, {'start': '2602.299', 'end': '2606.637', 'text': 'we can prove this here with what'}, {'start': '2602.899', 'end': '2606.637', 'text': 'we did, look.'}, {'start': '2607.738', 'end': '2613.710', 'text': 'Ah the slope here must be'}, {'start': '2608.338', 'end': '2616.846', 'text': 'positive Ah yes it was positive.  The'}, {'start': '2612.809', 'end': '2617.414', 'text': 'slope here must be'}, {'start': '2613.309', 'end': '2623.721', 'text': 'negative. Ah yes, the'}, {'start': '2613.777', 'end': '2623.721', 'text': 'slope was negative.  In this one it'}, {'start': '2616.913', 'end': '2623.721', 'text': 'has this shape the slope'}, {'start': '2617.480', 'end': '2623.721', 'text': 'was positive.  Yes'}, {'start': '2628.892', 'end': '2638.869', 'text': 'The slope is positive when it'}, {'start': '2629.492', 'end': '2642.839', 'text': 'has this inclination?  The'}, {'start': '2632.929', 'end': '2643.406', 'text': 'slope is negative?'}, {'start': '2637.935', 'end': '2647.845', 'text': '>> Daniela Rojas: Yes'}, {'start': '2638.936', 'end': '2647.845', 'text': '>> Professor Alberto Argon:'}, {'start': '2642.906', 'end': '2647.845', 'text': "Let's see. Let's do this. I'm not"}, {'start': '2643.473', 'end': '2647.845', 'text': 'going to give it to you now.'}, {'start': '2648.946', 'end': '2653.884', 'text': "I'm going to give you the coordinates of the graph"}, {'start': '2649.479', 'end': '2653.884', 'text': '.'}, {'start': '2656.987', 'end': '2664.962', 'text': "Because it's already Ah Let's put"}, {'start': '2657.587', 'end': '2664.962', 'text': 'minus two.  point four'}, {'start': '2666.063', 'end': '2673.971', 'text': 'Minus two point four.  And that'}, {'start': '2669.199', 'end': '2673.971', 'text': 'point B has coordinates.'}, {'start': '2675.072', 'end': '2679.977', 'text': '5 comma'}, {'start': '2685.115', 'end': '2693.057', 'text': 'Well we can go to the'}, {'start': '2685.582', 'end': '2693.057', 'text': 'Cartesian plane.  Yes,'}, {'start': '2694.158', 'end': '2702.465', 'text': "but if we don't want to."}, {'start': '2694.558', 'end': '2702.899', 'text': '>> Daniela Rojas: Yes'}, {'start': '2697.194', 'end': '2709.239', 'text': ">> Professor Alberto Argon: Let's"}, {'start': '2697.794', 'end': '2709.672', 'text': 'record ourselves.  That one of the'}, {'start': '2702.532', 'end': '2715.379', 'text': 'two points will have'}, {'start': '2702.966', 'end': '2720.184', 'text': 'x1 coordinates.  comma x2 And the'}, {'start': '2709.305', 'end': '2720.184', 'text': 'other point is going to have'}, {'start': '2709.739', 'end': '2720.184', 'text': 'coordinates.  x two Comma and two'}, {'start': '2715.445', 'end': '2720.184', 'text': 'Sorry I made a mistake above.'}, {'start': '2721.285', 'end': '2726.223', 'text': 'Two here was x and one.'}, {'start': '2730.327', 'end': '2742.406', 'text': 'So the point above'}, {'start': '2730.860', 'end': '2747.744', 'text': 'has coordinates x one And the'}, {'start': '2733.429', 'end': '2764.627', 'text': 'point below has'}, {'start': '2733.830', 'end': '2773.470', 'text': 'coordinates.  x two and two to'}, {'start': '2742.472', 'end': '2778.475', 'text': 'take out Nothing else we are going to do.'}, {'start': '2751.381', 'end': '2778.475', 'text': 'G2 minus 1 over x2 minus x1'}, {'start': '2768.465', 'end': '2778.475', 'text': 'And so we get the slope.'}, {'start': '2773.537', 'end': '2778.475', 'text': 'How much is Y two?'}, {'start': '2779.576', 'end': '2787.551', 'text': '>> Daniela Rojas: Not three minus'}, {'start': '2780.176', 'end': '2792.589', 'text': 'three.'}, {'start': '2784.615', 'end': '2793.189', 'text': '>> Professor Alberto Argon: less than'}, {'start': '2785.215', 'end': '2797.594', 'text': 'one'}, {'start': '2787.618', 'end': '2802.599', 'text': '>> Daniela Rojas: four'}, {'start': '2792.656', 'end': '2803.199', 'text': '>> Professor Alberto Argon: now x'}, {'start': '2797.661', 'end': '2806.236', 'text': '>> Daniela Rojas: five'}, {'start': '2802.666', 'end': '2808.638', 'text': '>> Professor Alberto Argon: less x1'}, {'start': '2805.736', 'end': '2813.644', 'text': '>> Daniela Rojas: Less less.'}, {'start': '2808.705', 'end': '2813.644', 'text': '>> Professor Alberto Argon: Minus'}, {'start': '2809.272', 'end': '2813.644', 'text': "minus two, that's right."}, {'start': '2817.748', 'end': '2822.686', 'text': "Now let's do the math."}, {'start': '2818.348', 'end': '2822.686', 'text': 'What is minus three, minus'}, {'start': '2818.882', 'end': '2822.686', 'text': 'four?'}, {'start': '2824.788', 'end': '2829.726', 'text': '>> Daniela Rojas: 7'}, {'start': '2831.828', 'end': '2837.834', 'text': '>> Professor Alberto Argon: And how much'}, {'start': '2832.428', 'end': '2838.434', 'text': 'is 5 minus times minus plus five'}, {'start': '2832.995', 'end': '2841.805', 'text': 'plus two.'}, {'start': '2836.900', 'end': '2846.009', 'text': '>> Daniela Rojas: 7'}, {'start': '2837.901', 'end': '2850.814', 'text': '>> Professor Alberto Argon: Then'}, {'start': '2838.501', 'end': '2850.814', 'text': 'the slope will remain for me.'}, {'start': '2841.872', 'end': '2850.814', 'text': 'minus seven divided by How much is'}, {'start': '2846.075', 'end': '2850.814', 'text': 'minus seven divided by seven.'}, {'start': '2853.951', 'end': '2863.560', 'text': '>> Daniela Rojas: thousands'}, {'start': '2857.988', 'end': '2864.160', 'text': '>> Professor Alberto Argon: Minus'}, {'start': '2858.555', 'end': '2867.297', 'text': 'one and the slope is less.  And'}, {'start': '2863.026', 'end': '2871.935', 'text': 'now we are going to get the equation by'}, {'start': '2863.627', 'end': '2871.935', 'text': 'grabbing any of the two'}, {'start': '2864.227', 'end': '2871.935', 'text': 'points on side B, which point do you'}, {'start': '2867.363', 'end': '2871.935', 'text': 'want to grab?'}, {'start': '2873.003', 'end': '2877.975', 'text': 'five point'}, {'start': '2879.076', 'end': '2885.015', 'text': "Minus three and we're going to use the"}, {'start': '2879.643', 'end': '2885.015', 'text': 'slope that it gave us.  Minus'}, {'start': '2880.243', 'end': '2885.015', 'text': 'one.'}, {'start': '2886.116', 'end': '2900.130', 'text': 'And we said the equation was y'}, {'start': '2886.716', 'end': '2900.130', 'text': 'minus y one.  It is equal to m.  by'}, {'start': '2894.223', 'end': '2900.130', 'text': 'x minus x1'}, {'start': '2901.231', 'end': '2909.139', 'text': 'We change the values \u200b\u200bof x1 y1 and'}, {'start': '2901.831', 'end': '2909.139', 'text': 'the slope.  would be'}, {'start': '2911.241', 'end': '2916.213', 'text': 'less how much'}, {'start': '2918.315', 'end': '2928.024', 'text': '>> Daniela Rojas: 4'}, {'start': '2923.320', 'end': '2930.526', 'text': '>> Professor Alberto Argon: And One is'}, {'start': '2923.887', 'end': '2935.532', 'text': 'Worth Four.  No, but'}, {'start': '2927.557', 'end': '2937.334', 'text': "we're already here, forget about"}, {'start': '2928.091', 'end': '2939.336', 'text': 'these two points.  You already'}, {'start': '2930.593', 'end': '2944.308', 'text': "gave me a point here and it wasn't the"}, {'start': '2935.599', 'end': '2944.308', 'text': 'return'}, {'start': '2937.401', 'end': '2944.308', 'text': '>> Daniela Rojas: worth 5'}, {'start': '2939.403', 'end': '2944.308', 'text': '>> Professor Alberto Argon: no'}, {'start': '2948.412', 'end': '2953.383', 'text': "It's less."}, {'start': '2960.490', 'end': '2965.429', 'text': 'This is equal to the slope'}, {'start': '2961.023', 'end': '2965.429', 'text': 'minus one.'}, {'start': '2967.531', 'end': '2976.440', 'text': 'For x and how much is x worth one?'}, {'start': '2971.568', 'end': '2976.440', 'text': '>> Daniela Rojas: 5'}, {'start': '2978.575', 'end': '2993.557', 'text': '>> Professor Alberto Argon: We remove'}, {'start': '2979.175', 'end': '2993.557', 'text': 'the parentheses and it would be plus'}, {'start': '2981.644', 'end': '2993.557', 'text': 'three.  Here we apply'}, {'start': '2986.015', 'end': '2993.557', 'text': 'distributive property.  Minus x.'}, {'start': '2996.660', 'end': '3001.598', 'text': 'From here we clear the and the 3'}, {'start': '2997.227', 'end': '3001.598', 'text': 'goes by subtracting.  would be'}, {'start': '3006.703', 'end': '3028.725', 'text': 'Minus x.  Plus 5 minus.  It would be done'}, {'start': '3015.878', 'end': '3028.725', 'text': 'now.  Plus Two then yes I'}, {'start': '3024.187', 'end': '3028.725', 'text': 'want her.'}, {'start': '3031.862', 'end': '3036.767', 'text': '>> Daniela Rojas: On the two.'}, {'start': '3043.874', 'end': '3048.812', 'text': 'Or in the minus 2 Well in which'}, {'start': '3044.474', 'end': '3048.812', 'text': 'the two are cut.'}, {'start': '3049.913', 'end': '3054.885', 'text': '>> Professor Alberto Argon: And now'}, {'start': '3050.446', 'end': '3054.885', 'text': 'we can graph, I say if'}, {'start': '3050.980', 'end': '3054.885', 'text': 'we need it or not.'}, {'start': '3055.986', 'end': '3060.891', 'text': 'Well, that would be what I'}, {'start': '3056.519', 'end': '3060.891', 'text': 'need, the equation of the'}, {'start': '3057.020', 'end': '3060.891', 'text': 'line.'}, {'start': '3186.616', 'end': '3191.521', 'text': '>> Daniela Rojas: Ready'}, {'start': '3195.659', 'end': '3200.630', 'text': '>> Professor Alberto Argon: Look at the'}, {'start': '3196.259', 'end': '3200.630', 'text': 'graph, it would look like this.'}, {'start': '3215.779', 'end': '3220.684', 'text': 'We are cutting point A at'}, {'start': '3221.818', 'end': '3229.892', 'text': 'minus two four when the'}, {'start': '3222.385', 'end': '3237.801', 'text': 'coordinates of point A and point'}, {'start': '3222.985', 'end': '3237.801', 'text': 'B are five minus three and when'}, {'start': '3226.089', 'end': '3237.801', 'text': 'joining them, it is cutting.  At'}, {'start': '3229.959', 'end': '3237.801', 'text': 'least in two.  Yes'}, {'start': '3239.903', 'end': '3242.805', 'text': 'So it is true,'}, {'start': '3240.470', 'end': '3243.372', 'text': 'what we said came true Yes, what'}, {'start': '3241.070', 'end': '3244.841', 'text': 'we said came true.'}, {'start': '3241.871', 'end': '3247.877', 'text': '>> Daniela Rojas: yes'}, {'start': '3242.872', 'end': '3248.444', 'text': '>> Professor Alberto Argon: any'}, {'start': '3243.439', 'end': '3249.045', 'text': 'questions'}, {'start': '3244.908', 'end': '3256.919', 'text': '>> Daniela Rojas: no'}, {'start': '3247.944', 'end': '3257.419', 'text': '>> Professor Alberto Argon: I know'}, {'start': '3248.511', 'end': '3260.957', 'text': 'that there are still many questions'}, {'start': '3249.111', 'end': '3261.557', 'text': 'but'}, {'start': '3256.986', 'end': '3264.427', 'text': '>> Daniela Rojas: Here we'}, {'start': '3257.486', 'end': '3269.498', 'text': 'get the equation, see.'}, {'start': '3261.024', 'end': '3273.937', 'text': '>> Professor Alberto Argon: Yes, of'}, {'start': '3261.624', 'end': '3273.937', 'text': "course. Or what did we do here in the end?   Let's"}, {'start': '3268.998', 'end': '3273.937', 'text': 'see what we did here in the'}, {'start': '3269.565', 'end': '3273.937', 'text': 'end, what did we get?'}, {'start': '3282.112', 'end': '3287.050', 'text': '>> Daniela Rojas: minus x plus'}, {'start': '3282.679', 'end': '3287.050', 'text': 'there would be minus x plus two and'}, {'start': '3289.152', 'end': '3291.687', 'text': '>> Professor Alberto Argon: Not plus'}, {'start': '3289.719', 'end': '3292.088', 'text': 'two and not and it is equal to minus x'}, {'start': '3290.286', 'end': '3292.555', 'text': 'plus two.'}, {'start': '3291.154', 'end': '3292.989', 'text': '>> Daniela Rojas: this is how it would be noticed'}, {'start': '3292.155', 'end': '3297.960', 'text': '>> Professor Alberto Argon:'}, {'start': '3292.622', 'end': '3299.228', 'text': "Remember, that's called"}, {'start': '3293.056', 'end': '3303.532', 'text': 'slope.  Yes because it is called'}, {'start': '3297.493', 'end': '3307.236', 'text': 'slope ordinate at the origin.'}, {'start': '3298.027', 'end': '3307.670', 'text': 'How much is the slope?  minus'}, {'start': '3299.295', 'end': '3312.108', 'text': 'one.  And what is the point where it'}, {'start': '3303.599', 'end': '3312.108', 'text': 'cuts the y-axis in two?  It is the'}, {'start': '3307.303', 'end': '3312.108', 'text': 'equation of the line.'}, {'start': '3307.736', 'end': '3312.108', 'text': '>> Daniela Rojas: Okay.'}, {'start': '3320.250', 'end': '3327.223', 'text': 'Thank you.'}, {'start': '3322.285', 'end': '3327.223', 'text': '>> Professor Alberto Argon: Any'}, {'start': '3322.852', 'end': '3327.223', 'text': 'other questions?'}, {'start': '3329.325', 'end': '3334.264', 'text': 'Finish copying.'}]