# How do you write the point slope form of the equation given (-4,0) parallel to y=3/4x-2?

Feb 22, 2017

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{\frac{3}{4}} \left(x + \textcolor{red}{4}\right)$

#### 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.

$y = \textcolor{red}{\frac{3}{4}} x - \textcolor{b l u e}{2}$

Therefore the slope of this line is $\textcolor{red}{m = \frac{3}{4}}$

Because the line we are looking for is parallel to the line in the problem we know it will have the same slope.

We can now use the point-slope formula to find the equation for the line we are looking for. 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 point from the problem and the slope from the parallel line gives:

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{\frac{3}{4}} \left(x - \textcolor{red}{- 4}\right)$

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{\frac{3}{4}} \left(x + \textcolor{red}{4}\right)$