# Question #cc23e

Feb 23, 2017

$\left(y + \textcolor{red}{18}\right) = \textcolor{b l u e}{- 4} \left(x - \textcolor{red}{4}\right)$

Or

$y = \textcolor{red}{- 4} x - \textcolor{b l u e}{2}$

#### Explanation:

The line in the equation is in slope-intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value. Therefore we know the slope is $- 4$.

We can now use the point-slope formula to find an equation for the line in the 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 slope and point from the problem gives:

$\left(y - \textcolor{red}{- 18}\right) = \textcolor{b l u e}{- 4} \left(x - \textcolor{red}{4}\right)$

$\left(y + \textcolor{red}{18}\right) = \textcolor{b l u e}{- 4} \left(x - \textcolor{red}{4}\right)$

Or, we can solve for $y$ to put the equation in slope-intercept form:

$y + \textcolor{red}{18} = \left(\textcolor{b l u e}{- 4} \times x\right) - \left(\textcolor{b l u e}{- 4} \times \textcolor{red}{4}\right)$

$y + \textcolor{red}{18} = - 4 x - \left(- 16\right)$

$y + \textcolor{red}{18} = - 4 x + 16$

$y + \textcolor{red}{18} - 18 = - 4 x + 16 - 18$

$y + 0 = - 4 x - 2$

$y = \textcolor{red}{- 4} x - \textcolor{b l u e}{2}$