# How do you write an equation in point-slope form for the given (–2, 1) and (4, 13)?

Aug 2, 2015

Use the slope formula to find slope $m = 2$, then use the second point to get:

$y - 13 = 2 \left(x - 4\right)$

#### Explanation:

Given two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$, then the slope $m$ of a line through those two points is given by the formula:

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

In our case, let $\left({x}_{1} , {y}_{1}\right) = \left(- 2 , 1\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(4 , 13\right)$. Then:

$m = \frac{13 - 1}{4 - \left(- 2\right)} = \frac{12}{6} = 2$

Then point slope form for a line is:

$y - {y}_{0} = m \left(x - {x}_{0}\right)$ where $m$ is the slope and $\left({x}_{0} , {y}_{0}\right)$ is some point on the line. To avoid double minus signs, let's use the second point $\left(4 , 13\right)$ to get:

$y - 13 = 2 \left(x - 4\right)$