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

Sep 25, 2016

$y = - \frac{3}{5} x + 2$

#### Explanation:

The point-slope form formula is:
$y - {y}_{1} = m \left(x - {x}_{1}\right)$

First me need to find $m$, the slope. We do this by using the slope formula which is:
$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

Now we plug in our points:
$\left({x}_{1} = - 5 , {x}_{2} = 0 , {y}_{1} = 5 , \mathmr{and} {y}_{2} = 2\right)$

 m = (2-5)/(0-(-5)

When we simplify we get our slope, which is:
$m = - \frac{3}{5}$

To find ${y}_{1}$ and ${x}_{1} ,$ we can use the original points we were given.
I'm going to use ${y}_{1} = 2$ and ${x}_{1} = 0$. (You can use ${y}_{1} = - 5$ and $x = 5$ if you want, the final answer will be the same.)

Now we plug all of this information into the point-slope formula
$y - 2 = - \frac{3}{5} \left(x - 0\right)$

We combine like terms on the left side and distribute $- \frac{3}{5}$ into the parenthesis ($- \frac{3}{5}$ multiplied with $x$ and $0$).

$y - 2 = - \frac{3}{5} x + 0$

Now we isolate the $y$ by adding 2 to both sides.

$y - 2 + 2 = - \frac{3}{5} x + 2$

When we simplify we get:
$y = - \frac{3}{5} x + 2$