# Question #76df0

Dec 18, 2016

The equation would be $y = m x + b$

#### Explanation:

B is the y intercept, the point of the line that touches some part of the y-axis.

M is the slope (rise over run). You find it by plugging two points on the line into the slope equation: $m = \frac{{y}_{2} - {y}_{1}}{{X}_{2} - {x}_{1}}$.

Y is basically the linear function.

So if I have a line with the equation: $y = 2 x + 1$

I can plug in values for $x$ and $y$ (let's say 1). I replace $x$ with 1 so --> $y = 2 \left(1\right) + 1$. SO if $x$ is 1, then I can solve the equation and say $y = 3$. That's one point (1, 3) on the line of the equation above. Another value to find another point. $b$ is 1 because $y$ = 2$x$ + 1. That means at (x, $1$) the line touches the y-axis.

And as I gave the equations above, when you find the second coordinate (the first being (1, 3)) by plugging in another value for $x$ and solving for $y$, you can find $m$, the slope.

Dec 18, 2016

Perhaps the question refers to the "intercept form" of a line:

$\frac{x}{a} + \frac{y}{b} = 1$,
where the $x$ intercept is $\left(a , 0\right)$ and the $y$ intercept is $\left(0 , b\right)$.

To convert this form to slope intercept form $y = m x + b$ (where $m$ is the slope and $b$ is the $y$ intercept),

multiply the equation $\frac{x}{a} + \frac{y}{b} = 1$ by the LCD $a b$

$a b \left(\frac{x}{a} + \frac{y}{b} = 1\right)$

$\frac{a b x}{a} + \frac{a b y}{b} = a b$

$b x + a y = a b$
$- b x \textcolor{w h i t e}{a a a} - b x$

$a y = - b x + a b$

$\frac{a y}{a} = \frac{- b x}{a} + \frac{a b}{a}$

$y = \left(- \frac{b}{a}\right) x + b$

So, to convert from the "intercept form" of a line $\frac{x}{a} + \frac{y}{b} = 1$
to the "slope intercept form" $y = m x + b$,

the slope $m = - \frac{b}{a}$ and the y intercept $b$ is equal to the "b" in the intercept form.
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