Answer
$y=\dfrac{4}{3}x-12$
Work Step by Step
RECALL:
(1) The point-slope form of a line's equation is $y−y_1=m(x−x_1)$ where m=slope and $(x_1, y_1)$ is a point on the line.
(2) The slope-intercept form of a line's equation is $y=mx+b$ where m=slope and b is the y-coordinate of the line's y-intercept.
(3) Parallel lines have equal slopes.
(4) Perpendicular lines have slopes whose product is $−1$ (negative reciprocals of each other).
The line is perpendicular to $y=−\frac{3}{4}x+1$. Since the slope of this line is $−\frac{3}{4}$, then the slope of the line perpendicular to it is the negative reciprocal of $−\frac{3}{4}$, which is $\frac{4}{3}$.
Using the given point on the line $(0, −12)$ and the slope $\frac{4}{3}$, the equation of the line in slope-intercept form is:
$y=\dfrac{4}{3}x+(-12)
\\y=\dfrac{4}{3}x-12$
