# How do you write an equation in point-slope form for the given (–3, –5) and (3, 0)?

Jul 27, 2015

The point-slope form is $y + 5 = \frac{5}{6} \left(x + 3\right)$.

#### Explanation:

First determine the slope from the two points using the slope equation $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$, where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are the two points.

$\left({x}_{1} , {y}_{1}\right) = \left(- 3 , - 5\right)$

$\left({x}_{2} , {y}_{2}\right) = \left(3 , 0\right)$

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

$m = \frac{0 - \left(- 5\right)}{3 - \left(- 3\right)}$ =

$m = \frac{5}{6}$

Now use the slope and one point in order to write the linear equation in point-slope form. The general equation for the point-slope form is $y - {y}_{1} = m \left(x - {x}_{1}\right)$. where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ is one of the two points.

#m=5/6

Point=$\left(- 3 , - 5\right)$

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - \left(- 5\right) = \frac{5}{6} \left(x - \left(- 3\right)\right)$ =

$y + 5 = \frac{5}{6} \left(x + 3\right)$