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

Jul 23, 2015

Determine the slope from the 2 points then use that together with one of the points to write the point-slope form equation

#### Explanation:

Step 1: Find the slope of the line through $\left(- 2 , - 1\right)$ and $\left(4 , - 4\right)$
Given two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ the slope of the line through them is:
$\textcolor{w h i t e}{\text{XXXX}}$$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

For the given values this becomes:
$\textcolor{w h i t e}{\text{XXXX}}$$m = \frac{- 4 - \left(- 1\right)}{4 - \left(- 2\right)} = - \frac{1}{2}$

Step 2: Insert the calculated slope and one of the points into the general slope-point form
The general slope-point form is
$\textcolor{w h i t e}{\text{XXXX}}$$y - \hat{y} = m \left(x - \hat{x}\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$for a line with slope $m$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$through the point $\left(\hat{x} , \hat{y}\right)$

Using $\left(- 2 , - 1\right)$ as $\left(\hat{x} , \hat{y}\right)$ and the slope from Step 1:
$\textcolor{w h i t e}{\text{XXXX}}$$y - \left(- 1\right) = \left(- \frac{1}{2}\right) \left(x - \left(- 2\right)\right)$