# How do you graph using slope and intercept of 6x - 3y = -12?

Nov 1, 2015

$6 x - 3 y = - 12$ has a slope of $2$ and a y-intercept of $4$
Starting at the y-intercept $\left(0 , 4\right)$ plot points by repetitively going 1 step right and 2 steps up.

#### Explanation:

The y-intercept is the value of $y$ when $x = 0$
For $6 x - 3 y = - 12$ when $x = 0$
$\textcolor{w h i t e}{\text{XXX}} 6 \left(0\right) - 3 y = - 12 \Rightarrow y = 4$
So the y-intercept is at $\left(0 , 4\right)$

The slope for an equation in the form
$\textcolor{w h i t e}{\text{XXX}} A x + B y = C$
is $m = - \frac{A}{B}$
So the slope of
$\textcolor{w h i t e}{\text{XXX}} 6 x - 3 y = - 12$
is $m = - \frac{6}{- 3} = 2$

A slope of $2$ means that for every steep in the positive $x$ direction the value of $y$ must increase by $2$

graph{(6x-3y+12)(x^2+(y-4)^2-0.01)((x-1)^2+(y-6)^2-0.01)((x-2)^2+(y-8)^2-0.01)=0 [-2.505, 17.495, -0.6, 9.4]}