Answer:
[tex]y + 2 = -\frac{4}{3}(x-4)[/tex]
Step-by-step explanation:
A perpendicular line is a line which has a negative reciprocal slope to the line. The slope can be found by writing the ratio between vertical and horizontal distance between the points.
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{1--2}{8-4}=\frac{3}{4}[/tex]
This means the slope of the perpendicular line will be -4/3.
Substitute m = -4/3 and (4,-2) into the point slope form of a linear equation.
[tex]y - -2 = -\frac{4}{3}(x - 4)\\y + 2 = -\frac{4}{3}(x-4)[/tex]
