# How do you write an equation of a line with Slope = -5, passing through (-4, -2)?

Mar 2, 2018

$y = - 5 x - 22$

#### Explanation:

The point-slope form of a line is given by the formula

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

Where $\left({x}_{1} , {y}_{1}\right)$ is a point through which the line passes and $m$ is the line's slope. We have all information required to use this formula, so let's simply plug in $\left({x}_{1} , {y}_{1}\right) = \left(- 4 , - 2\right) , m = - 5$ into the above formula:

$y - \left(- 2\right) = - 5 \left(x - \left(- 4\right)\right)$

Simplify.

$y + 2 = - 5 \left(x + 4\right)$

(Subtracting a negative is the same as adding)

$y + 2 = - 5 x + 4 \left(- 5\right)$

Distributive Property.

$y + 2 = - 5 x - 20$

Solve for $y :$

$y \cancel{+ 2 - 2} = - 5 x - 20 - 2$

$y = - 5 x - 22$