# How do you write the equation in slope intercept form given (10,-9);m=-2?

Apr 24, 2018

$y = - 2 x - 19$

#### 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 $\left(10 , - 9\right)$

$m = - 2$
${x}_{1} = 10$
${y}_{1} = - 9$

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

Plug in the values
$y - \left(- 9\right) = - 2 \left(x - 10\right)$

Simplify the signs
$y + 9 = - 2 \left(x + 10\right)$

Use distributive property to eliminate the parenthesis
$y + 9 = - 2 x - 20$

Use the additive inverse to isolate the $y$ value
$y \cancel{+ 9} \cancel{- 9} = - 2 x - 10 - 9$

Simplify the common terms
$y = - 2 x - 19$