# What is the equation of the line with slope  m= -5  that passes through  (-1,-3) ?

Apr 24, 2018

$y = - 5 x - 8$

#### Explanation:

Since we are provided the slope and a point on the line we can use the equation for point slope form of the equation of a line.

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

Where $m =$ slope and the point is $\left({x}_{1} , {y}_{1}\right)$

For this situation $m = - 5$ and a point of $\left(- 1 , - 3\right)$

$m = - 5$
${x}_{1} = - 1$
${y}_{1} = - 3$

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

Plug in the values
$y - \left(- 3\right) = - 5 \left(x - \left(- 1\right)\right)$

Simplify the signs
$y + 3 = - 5 \left(x + 1\right)$

Use distributive property to eliminate the parenthesis
$y + 3 = - 5 x - 5$

Use the additive inverse to isolate the $y$ value
$y \cancel{+ 3} \cancel{- 3} = - 5 x - 5 - 3$

Simplify the common terms
$y = - 5 x - 8$