# Determine if this equation is perpendicular? -4x+2y=12 x+2y=6

## Can you please show the steps. Thank you

Mar 16, 2017

These two equations represent line which are perpendicular.

#### Explanation:

Any equation of the form:
$\textcolor{w h i t e}{\text{XXX")Ax+By=Ccolor(white)("XX}}$ has a slope of $\textcolor{w h i t e}{\text{XX}} - \frac{A}{B}$

Therefore
{: (-4x+2y=12," has a slope of ",-(-4)/2=2), (," and",), (x+2y=6," has a slope of ",-1/2) :}

Two lines are perpendicular if the slope of one is the negative inverse of the slope of the other. The negative inverse of $2$ is $- \frac{1}{2}$, so these lines are perpendicular.