# How do you write an equation in standard form given a line that passes through (-6,-3), with m=-1/2?

May 28, 2015

Given that the required line passes through $\left(- 6 , - 3\right)$ and has a slope of $m = - \frac{1}{2}$
we can first write the line's equation in slope-point form
and then convert this to standard form

Slope-Point Form
For a slope of $m$ and a point $\left(\hat{x} , \hat{y}\right)$ the general slope-point form is:
$\left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$

With the given values this becomes
$\left(y + 3\right) = \left(- \frac{1}{2}\right) \left(x + 6\right)$

Standard Form
Assuming the standard form for a linear equation is
$A x + B y = C$ with $A \ge 0 \mathmr{and} A \epsilon \mathbb{Z}$

we can re-arrange our slope-point solution:

$2 \left(y + 3\right) = - x - 6$

$x + 2 y + 6 = - 6$

$\left(1\right) x + \left(2\right) y = - 12$ (standard form)