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 Question from Conor, a student: Hi! I was wondering if you could help me with this question :) Thanks are these lines parallel? y = 3x -2 and 6y = 3x +2

Hi Conor.

Parallel lines have the same slope. If you turn both equations into the y = mx+b form (the first equation is already in this form) then you can compare the "m" values. If they are the same, and the sign (pos/neg) is the same and the values of "b" are different, then the lines are parallel.

Example: Are these lines parallel? y = 0.6x - 4 and 8 = 3x - 5y
Solution: first change the second equation into y = mx + b form:

8 = 3x - 5y
5y = 3x - 8
y = (3/5)x - (8/5)
m = 3/5 = 0.6

This is the same as the m in the first equation, so yes, these two lines are parallel.

You try yours using the same idea.

Hope this helps,
Stephen La Rocque

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
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