# How do you write the point slope form of the equation given (0,-5) and (-2,4)?

Sep 11, 2016

Use the equation of the point-slope form.

#### Explanation:

The equation of point-slope is

$y - {y}_{1} = m \left(x - {x}_{1}\right)$ where m is the slope and $\left({x}_{1} , {y}_{1}\right)$ is a point.

First find the slope using the two points $\left(0 , - 5\right)$ and $\left(- 2 , 4\right)$.

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{4 - - 5}{- 2 - 0} = \frac{9}{-} 2 = - \frac{9}{2}$

Choose either of the points (it doesn't matter which one) and plug it into the point-slope equation, along with the value of m.

I am choosing the first point $\left(0 , - 5\right)$ as $\left({x}_{1} , {y}_{1}\right)$

$y - - 5 = - \frac{9}{2} \left(x - 0\right)$
$y + 5 = - \frac{9}{2} \left(x - 0\right)$