# How do you graph the line through point (-3,-1) and slope m=-1/5?

Mar 23, 2017

$y = - \frac{1}{5} x + \frac{8}{5}$

#### Explanation:

We use the point-slope formula: $y - {y}_{1} = m \left(x - {x}_{1}\right)$

We know:
$m = - \frac{1}{5}$
A point: $\left(- 3 , - 1\right) \to \left({x}_{1} , {y}_{1}\right)$

Thus, we substitute all these values into the point-slope formula:

$y - \left(- 1\right) = - \frac{1}{5} \left(x - \left(- 3\right)\right) \to y + 1 = - \frac{1}{5} \left(x + 3\right)$

This gives us the equation of the line with the slope $- \frac{1}{5}$ that passes through the point $\left(- 3 , - 1\right)$ but if you need to write the equation in $y = m x + b$ then here's how we do it.

So we are simply solving for $y$

$y + 1 = - \frac{1}{5} \left(x + 3\right)$

$y + 1 = - \frac{1}{5} x - \frac{3}{5}$

$y = - \frac{1}{5} x - \frac{3}{5} - 1 \to y = - \frac{1}{5} x \left(- \frac{3}{5} - \frac{5}{5}\right)$

$y = - \frac{1}{5} x + \frac{8}{5}$

We can verify this graphically: graph{-1/5x-8/5 [-10, 10, -5, 5]}