# How do you write the equation in point slope form given ( -2 , 5 ) , ( 4 , -3 )?

Jun 1, 2017

Answers: $y - 5 = - \frac{4}{3} \left(x + 2\right)$ or $y + 3 = - \frac{4}{3} \left(x - 4\right)$

#### Explanation:

Write point-slope form of a linear equation given points $\left(- 2 , 5\right)$ and $\left(4 , - 3\right)$.

Note that the general form of point-slope form is:
$y - {y}_{1} = m \left(x - {x}_{1}\right)$ where $m$ is the slope of the line and $\left({x}_{1} , {y}_{1}\right)$ is a point on the line.

First, we need to find the slope, m:
We know that $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ with points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$
So, we can plug in our given values:
$m = \frac{5 - \left(- 3\right)}{- 2 - 4}$
$m = \frac{8}{- 6}$
$m = - \frac{4}{3}$

Now, we choose one of the points to write the equation in point slope form, (I will write both possible equations in point-slope form):
For $\left(- 2 , 5\right)$
$y - 5 = - \frac{4}{3} \left(x + 2\right)$

For $\left(4 , - 3\right)$
$y + 3 = - \frac{4}{3} \left(x - 4\right)$