A(0,2) and B(-8, 4)
x1 = 0; y1 = 2
x2 = -8; y2 = 4
The line that passes trhoug A and B will have this slope:
m = (y2 - y1)/(x2-x1) =(4 - 2)/(-8 - 0) = 2/-8 = -1/4 = -0.25
the equation of a line is y = mx + b
if we take the point A, this equation would be: 2 = m(0) + b
2 = b
so b = 2
the equation of the line is y = -0.25x + 2
the middle point between A and B is:
for x: (-8 - 0)/2 = -4
for y = (4 - 2)/2 = 2/2 = 1
so the middle point, the point where the bisector will pass is (-4, 1)
if the line is perpendicular, that means that its slope is -1/m of the original line
in this case -1/-0.25 = 4
if the slope is 4 and it passes throug (-4, 1), and using the equation y = mx + b with y = 1 and x = -1:
1 = 4(-1) + b
1 = -4 + b
1 + 4 = b
b = 5
so the final equation is y = 4x + 5
the answer is y = 4x + 5