# How do you write the point slope form of the equation given (4,-4) parallel to y=-x-4?

Mar 5, 2017

$\left(y + \textcolor{red}{4}\right) = \textcolor{b l u e}{- 1} \left(x - \textcolor{red}{4}\right)$

#### Explanation:

The equation in the problem 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: $y = \textcolor{red}{- 1} x - \textcolor{b l u e}{4}$ and $\textcolor{red}{m = - 1}$. A parallel line will have the same slope, or $m = - 1$

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 we derived and the point from the problem gives:

$\left(y - \textcolor{red}{- 4}\right) = \textcolor{b l u e}{- 1} \left(x - \textcolor{red}{4}\right)$

$\left(y + \textcolor{red}{4}\right) = \textcolor{b l u e}{- 1} \left(x - \textcolor{red}{4}\right)$