Answer:
y = [tex]\frac{4}{3} x[/tex] - 8
Step-by-step explanation:
The given line passes through (-4, 4) and (4, -2)
The slope of this line will be given by: Change in y ÷ change in x
Slope = [tex]\frac{4 - -2}{-4 - 4}[/tex] = [tex]-\frac{6}{8}[/tex] = [tex]-\frac{3}{4}[/tex]
The slope of the given line times the slope of the perpendicular line = -1
Let's say the slope of the perpendicular line is p
Then, [tex]-\frac{3}{4}[/tex] × p = -1
p = -1 ÷ [tex]-\frac{3}{4}[/tex] = [tex]\frac{4}{3}[/tex]
The perpendicular line passes through point (6, 0)
Taking another point (x, y) on the perpendicular line;
[tex]\frac{y - 0}{x - 6}[/tex] = [tex]\frac{4}{3}[/tex]
Cross multiplying this gives the equation of the perpendicular line to be:
y = [tex]\frac{4}{3} x[/tex] - 8
