How do you find the slope and intercept of -4x+2y=12?

Apr 10, 2016

Slope: $2$
y-intercept: $6$
(x-intercept: $- 3$)

Explanation:

slope
Given an equation in the form $A x + B y = C$ the slope is $\left(- \frac{A}{B}\right)$
So $- 4 x + 2 y = 12$ has a slope of $- \frac{- 4}{2} = 2$

Alternately, we could convert the given form
into "slope-intercept form": $y = m x + b$ with slope $m$ and y-intercept $b$
$\textcolor{w h i t e}{\text{XXX}} - 4 x + 2 y = 12$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow 2 y = 4 x + 12$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow y = 2 x + 6$

y-intercept
If we used the "slope-intercept form" (above) we already have the y-intercept: $6$;
otherwise we can determine the y-intercept by finding the value of $y$ when $x = 0$ in the given equation: $- 4 x + 2 y = 12$
$\textcolor{w h i t e}{\text{XXX}} - 4 \times \left(0\right) + 2 y = 12$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow y = 6$

x-intercept (note sometimes when "the intercept" is asked for, what is meant is only the y-intercept)
The x-intercept can be determined by find the value of $x$ when $y = 0$ in the given equation: $- 4 x + 2 y = 12$
$\textcolor{w h i t e}{\text{XXX}} - 4 x + 2 \times \left(0\right) = 12$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = - 3$