# How do you write the equation using function notation:? through (-4, -1); perpendicular to F(x)=2x-4?

May 26, 2015

The slope ($m$) of the original line is the coefficient of $x$, namely $2$

The slope of any perpendicular line will be $- \frac{1}{m}$, that is $- \frac{1}{2}$

So we're looking for $c$ so that

$G \left(x\right) = - \frac{1}{2} x + c$ satisfies $G \left(- 4\right) = - 1$

So:
$- 1 = G \left(- 4\right) = - \frac{1}{2} \left(- 4\right) + c = 2 + c$

Subtracting $2$ from both sides, we find $c = - 3$.

$G \left(x\right) = - \frac{1}{2} x - 3$