Answer
$4x-y = -5$
Work Step by Step
First, we solve for the slope of the perpendicular line:
$x+4y = 6 \\ y = -1/4 x - 3/2$
Since this is in slope intercept form, we see that the slope is -1/4. Thus, the slope of the perpendicular line is the opposite reciprocal, which is 4. Thus, we use point slope form, and then we simplify to standard form:
$y - y_{1} = m(x-x_{1}) \\y+3 = 4(x+2) \\ y + 3 = 4x +8 \\ 4x -y = -5 $
