# What is the slope-intercept form of the line that passes through (4, –7) and (13, –1)?

Oct 24, 2015

$y = \frac{2}{3} x - \frac{29}{3}$

#### Explanation:

Slope $= \frac{\Delta y}{\Delta x} = \frac{\left(- 1\right) - \left(- 7\right)}{13 - 4} = \frac{6}{9} = \frac{2}{3}$

Slope-point form: $\left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$

Using $\left(4 , - 7\right)$ as $\left(\hat{x} , \hat{y}\right)$ (and $\frac{2}{3}$ as the slope $m$):
$\textcolor{w h i t e}{\text{XXX}} y + 7 = \frac{2}{3} x - \frac{8}{3}$

Converting to slope intercept form:
$\textcolor{w h i t e}{\text{XXX}} y = \frac{2}{3} x - \frac{29}{3}$