How do you write an equation of the line in point slope form with (–1, –3) and (4, 1)?

Jun 26, 2015

$y - 1 = \frac{4}{5} \left(x - 4\right)$

Explanation:

Step 1: Find the slope
$m = \frac{\Delta y}{\Delta x} = \frac{1 - \left(- 3\right)}{4 - \left(- 1\right)} = \frac{4}{5}$

Step 2: Using either of the given points plug that point and the slope into the standard slope-point form for a line
Slope-point form:
$\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 slope of $m$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$and a point $\left(\hat{x} , \hat{y}\right)$

Using the point $\left(\hat{x} , \hat{y}\right) = \left(4 , 1\right)$ and the previously determined $m = \frac{4}{5}$

A slope-point form of the line is
$\textcolor{w h i t e}{\text{XXXX}}$$y - 1 = \frac{4}{5} \left(x - 4\right)$