Answer:
y = 3/2x-14
Explanation:
The given line is y=-2/3x. So, the slope of the given line is -2/3.
Now, we have to find the perpendicular line to y= -2/3x passing through the point (4,-8).
The product of two perpendicular lines is -1.
m1.m2 = -1.
-2/3.m2= -1
m2 = 3/2
Now, we need to find the equation of the line passing through the point (4,-8) with slope 3/2.
The equation of slope-point form is (y-y1) = m(x-x1)
y-(-8) = 3/2 (x-4)
y+8 = 3/2x -6
Now, we have to add 6 on both sides.
y + 8 + 6 = 3/2x - 6 + 6.
y + 14 = 3/2x
y = 3/2x - 14.