# Slope-Intercept Form

## Key Questions

$m$ is the slope, while $b$ is the y-intercept.

#### Explanation:

Any linear equation has the form of

$y = m x + b$

• $m$ is the slope of the equation

• $b$ is the y-intercept

The slope of the line, $m$, is found by

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

where $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are the coordinates of any two points in the line.

The y-intercept, $b$, is found by plugging in $x = 0$ into the equation, which results in $y = b$, and therefore is the y-intercept.

In some cases, if the equation is already arranged for you nicely, like $y = 3 x + 5$, we can easily find the y-intercept for this line, which is $5$.

Other times, the equation might not be arranged nicely, with cases such as $\frac{1}{2} x + 3 y = 5$, in which we solve for the y-intercept:

$\frac{1}{2} x + 3 y = 4$

$3 y = 4 - \frac{1}{2} x$

$y = \frac{- \frac{1}{2} x + 4}{3}$

$y = - \frac{1}{6} x + \frac{4}{3}$

So, the y-intercept of this line is $\frac{4}{3}$.

• The $y$-intercept $b$ can be found by reading the $y$-axis where the graph hits the y-axis, and the slope $m$ can be found by finding any two distinct points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ on the graph, and using the slope formula below.

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

I hope that this was helpful.

$y = m x + b$

Where:
$m$ is the slope of the line.
$b$ is the y-intercept of the line.

#### Explanation:

Consider $y = x$

graph{y=x [-10, 10, -5, 5]}

In this equation, the coefficient to $x$ is 1 and our y-intercept is 0.

We could think of that equation as looking like:

$y = 1 x + 0$

Notice that the graphed line has a "rise-over-run" of $\frac{1}{1}$ which is just 1 and the line passing through the y-axis at $y = 0$