# How do you write an equation in slope-intercept form of the line through point P(-10,1) with slope -5?

May 25, 2015

Since we're given the slope and a point, let's start with point slope form.

The point slope form is:

$y - {y}_{0} = m \left(x - {x}_{0}\right)$ where $m$ is the slope and $\left({x}_{0} , {y}_{0}\right)$ is a point through which the line passes.

In our case $m = - 5$ and $\left({x}_{0} , {y}_{0}\right) = \left(- 10 , 1\right)$, so we can write:

$y - 1 = - 5 \left(x - \left(- 10\right)\right) = - 5 \left(x + 10\right)$

Slope intercept form is:

$y = m x + c$ where $m$ is the slope and $c$ the intercept.

To rearrange in slope intercept form, add $1$ to both sides to get:

$y = - 5 \left(x + 10\right) + 1$

$= - 5 x - 50 + 1$

$= - 5 x - 49$

This is pretty much slope intercept form with slope $m = - 5$ and intercept $c = - 49$.

If we are really picky, we might write:

$y = - 5 x + - 49$

May 25, 2015

The equation in slope-intercept form is $y = - 5 x - 49$.

Slope-intercept form: $y = m x + b$, where $m$ is the slope and $b$ is the y-intercept.

Substitute the known values into the equation, then solve for $b$.

y=1 m$= - 5$
$x = - 10$

$y = m x + b$ =

$1 = - 5 \left(- 10\right) + b$ =

$1 = 50 + b$

$- 49 = b$

$y = - 5 x - 49$