How do you write an equation of a line with Slope =3,(4,-8)?

Jun 26, 2015

$y + 8 = 3 \left(x - 4\right)$
or in standard form $3 x - 1 y = 20$

Explanation:

Given a slope of $m = 3$ through a point $\left(\hat{x} , \hat{y}\right) = \left(4 , - 8\right)$
the slope-point form of a line:
$\textcolor{w h i t e}{\text{XXXX}}$$\left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$
becomes
$\textcolor{w h i t e}{\text{XXXX}}$$y - \left(- 8\right) = 3 \left(x - 4\right)$
or
$\textcolor{w h i t e}{\text{XXXX}}$$y + 8 = 3 \left(x - 4\right)$

While this is a perfectly correct answer, an equation in standard form might be more desirable.

$\textcolor{w h i t e}{\text{XXXX}}$$y + 8 = 3 x - 12$

$\textcolor{w h i t e}{\text{XXXX}}$$- 3 x + y + 8 = - 12$

$\textcolor{w h i t e}{\text{XXXX}}$$- 3 x + y = - 20$

$\textcolor{w h i t e}{\text{XXXX}}$$3 x - y = 20$ (in standard form)