# How do you find an equation of the line having the given slope and containing the given point m=-8, (4,5)?

Jan 3, 2017

Use the slope-point formula to complete this question. See full explanation below.

#### Explanation:

Because we have been given a slope and a point on the line we can use the point-slope formula to complete this problem.

The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the information we are provided gives us this equation:

$\left(y - \textcolor{red}{5}\right) = \textcolor{b l u e}{- 8} \left(x - \textcolor{red}{4}\right)$

If we want to put this in the more familiar form of the slope-intercept form we can solve for $y$ as follows:

y - color(red)(5) = color(blue)(-8)x - (color(blue)(-8) xx color(red)(4)))

$y - \textcolor{red}{5} = \textcolor{b l u e}{- 8} x - \left(- 32\right)$

$y - \textcolor{red}{5} = \textcolor{b l u e}{- 8} x + 32$

$y - \textcolor{red}{5} + 5 = \textcolor{b l u e}{- 8} x + 32 + 5$

$y - 0 = \textcolor{b l u e}{- 8} x + 37$

$y = - 8 x + 37$