# How do you write the point slope form of the equation given (-2,4) parallel to y=-5/2x+5?

Jun 3, 2017

See a solution process below:

#### 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.

$y = \textcolor{red}{- \frac{5}{2}} x + \textcolor{b l u e}{5}$

Therefore the slope of this line is: $\textcolor{red}{m = - \frac{5}{2}}$

Because the line we are looking for is parallel to this line by definition it will have the same slope.

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 determined and the values from the point in the problem gives:

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- \frac{5}{2}} \left(x - \textcolor{red}{- 2}\right)$

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- \frac{5}{2}} \left(x + \textcolor{red}{2}\right)$