# What is the equation in point-slope form and slope intercept form for the line given (–1, –3) and (4, 1)?

May 5, 2015

Given two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$
the slope is $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

For the given points $\left({x}_{1} , {y}_{1}\right) = \left(- 1 , - 3\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(4 , 1\right)$

$m = \frac{1 - \left(- 3\right)}{4 - \left(- 1\right)} = \frac{4}{5}$

Now that we have the slope we can use either of the given points to write a slope-point form for the equation:
$\left(y - 1\right) = \frac{4}{5} \left(x - 4\right)$

The slope intercept form is
$y = m x + b$
where $b$ is the y-intercept

Working with the previously developed slope-point form:
$\left(y - 1\right) = \frac{4}{5} \left(x - 4\right) = \frac{4}{5} x - \frac{16}{5}$

We obtain the slope-intercept form:
$y = \frac{4}{5} x - \frac{11}{5}$