# How do you write the slope-intercept equation for the line that passes through (1,-9) and (3,-1)?

Jan 23, 2017

$y = 4 x - 13$

#### Explanation:

Slope-intercept form of a linear function looks like this:

$y = \textcolor{p u r p \le}{m} x + \textcolor{b l u e}{b}$ where

$\textcolor{p u r p \le}{m} = \text{slope}$
$\textcolor{b l u e}{b} = y \text{-intercept}$

Using the given points, we can find the slope of the line:

$\text{slope} = \textcolor{p u r p \le}{m} = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{\left(- 1\right) - \left(- 9\right)}{3 - 1} = \frac{8}{2} = \frac{4}{1} = \textcolor{p u r p \le}{4}$

Putting this into our equation, we get:

$y = \textcolor{p u r p \le}{4} x + \textcolor{b l u e}{b}$

To find $b$, we can use one of the given points and the equation:

Let's use $\left(3 , - 1\right)$ and solve for $\textcolor{b l u e}{b}$:

$y = 4 x + \textcolor{b l u e}{b}$
$\textcolor{red}{- 1} = 4 \left(\textcolor{red}{3}\right) + \textcolor{b l u e}{b}$
$- 1 = \textcolor{red}{12} + \textcolor{b l u e}{b}$
$- 1 \textcolor{red}{- 12} = 12 \textcolor{red}{- 12} + \textcolor{b l u e}{b}$
$\textcolor{red}{- 13} = \textcolor{b l u e}{b}$

Putting this into our equation, we get:

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

or

$y = 4 x - 13$