# How do I write an equation for? Slope= -1/3, passing through (2,-7)

Jun 7, 2018

$y = - \frac{1}{3} x - \frac{19}{3}$

#### Explanation:

Let's start off with point-slope form.
$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$
where ${y}_{1}$ and ${x}_{1}$ are points on the line and $m$ is the slope.
We can plug in the information we have into this equation.
$y - \left(- 7\right) = - \frac{1}{3} \left(x - 2\right)$
or
$y + 7 = - \frac{1}{3} \left(x - 2\right)$
If you want to convert this to slope-intercept form, you would simply solve for y
$y + 7 = - \frac{1}{3} x + \frac{2}{3}$

$y = - \frac{1}{3} x - \frac{19}{3}$