# What is the slope intercept form of the line passing through (12,7)  with a slope of -1/5 ?

Jan 23, 2016

$y = - \frac{1}{5} x + \frac{47}{5}$

#### Explanation:

Given
Slope $- \frac{1}{5}$
Point $\left(12 , 7\right)$

The slope-point form of the line given slope $m$ and point $\left({x}_{1} , {y}_{1}\right)$ is

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

Let us plug in the given values

$y - 7 = - \frac{1}{5} \left(x - 12\right)$

Remember this is not what we need. We need the equation to be in slope intercept form.

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

We now have to simplify our equation from slope point form to get our answer.
$y - 7 = - \frac{1}{5} x + \frac{12}{5}$ $\quad$ distributing $- \frac{1}{5}$
Adding 7 to both the side

$y = - \frac{1}{5} x + \frac{12}{5} + 7$

$y = - \frac{1}{5} x + \frac{47}{5}$ answer.