# What is the equation of the line through point (2, -3) with slope -4?

Nov 21, 2015

$4 x + y = 5$

#### Explanation:

The general slope-point for a line with slope $m$ through a point $\left(\hat{x} , \hat{y}\right)$ is
$\textcolor{w h i t e}{\text{XXX}} \left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$

Given
$\textcolor{w h i t e}{\text{XXX}} m = \left(- 4\right)$
$\textcolor{w h i t e}{\text{XXX}} \left(\hat{x} , \hat{y}\right) = \left(2 , - 3\right)$
the slope-point form of the line is
$\textcolor{w h i t e}{\text{XXX}} \left(y + 3\right) = \left(- 4\right) \left(x - 2\right)$

Converting to standard form:
$\textcolor{w h i t e}{\text{XXX}} y + 3 = - 4 x + 8$

$\textcolor{w h i t e}{\text{XXX}} 4 x + y = 5$