# The equation of line CD is y = −2x − 2. How do you write an equation of a line parallel to line CD in slope-intercept form that contains point (4, 5)?

May 2, 2017

$y = - 2 x + 13$
See explanation this is a long answer question.

#### Explanation:

CD:$\text{ } y = - 2 x - 2$

Parallel means the new line (we will call it AB) will have the same slope as CD. $\text{ } m = - 2$

$\therefore y = - 2 x + b$

Now plug in the given point. $\left(x , y\right)$

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

Solve for b.

$5 = - 8 + b$

$13 = b$

So the equation for AB is

$y = - 2 x + 13$

Now check

$y = - 2 \left(4\right) + 13$
$y = 5$

Therefore $\left(4 , 5\right)$ is on the line $y = - 2 x + 13$