# How do you write an equation in standard form given a line that passes through (-5,-2) with slope -3?

May 27, 2015

Given the point $\left(- 5 , - 2\right)$ and the slope $\left(- 3\right)$ we can easily write the linear equation in slope-point form and then convert it to standard form.

Slope-Point Form
$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$ for a slope of $m$ and a point $\left({x}_{1} , {y}_{1}\right)$
becomes
$\left(y - \left(- 2\right)\right) = \left(- 3\right) \left(x - \left(- 5\right)\right)$
or
$y + 2 = \left(- 3\right) \left(x + 5\right)$

Standard Form
Standard form of a linear equation is
$A x + B y = C$ with $A \ge 0 \mathmr{and} A \epsilon \mathbb{Z}$
$y + 2 = \left(- 3\right) \left(x + 5\right)$
$\rightarrow y + 2 = - 3 x - 15$

$\rightarrow 3 x + 1 y = - 17$

which is in standard form