Answer
$y = -\frac{1}{3}x +\frac{5}{3}$
Work Step by Step
The first step is to find the slop of the line.
You know it is perpendicular to $3x-y = 4$ or $3x-4 = y$.
So it i perpendicular to a line with a slope of 3.
To find the slope of a perpendicular line, you find the negative reciprocal of the original line. In this case, it is $-\frac{1}{3}$.
Since it goes through the point $(-1,2)$, you can substitute -1 for $x$ and 2 for $y$ into the equation --> $y= -\frac{1}{3} x +b$. Then solve for b.
$2= -\frac{1}{3}(-1) +b$
$2-\frac{1}{3} = b$
$\frac{5}{3} = b$
So in the linear equation --> $y=mx+b$, $m = -\frac{1}{3}$ and $b=\frac{5}{3}$. The answer is thus:
$y = -\frac{1}{3}x +\frac{5}{3}$
