1st, let's find the equation on the graph and let A(-4,4) and B(4,-2):
This is a linear function y = mx +b, where m is the slope
a) Calculate m: m = (y₂-y₁)/(x₂-x₁), [ A(x₁, y₁) and B(x₂, y₂)
m= (-2-4)/[4-(-4)] = -6/8 and m= -3/4, the function becomes y =-3/4 + b
b) Calculate b: you replace the value of x and y in any of the A or B coordinates: Let's take B(4 ,-2) and plug in y=-3/4 + b;
-2 = (-3/4)(4) + b, b=1. So the equation in the graph is :
y = (-3/4).x +1
c) Find the line perpendicular to y =(-3/4).x + 1 and passing through C(6,0)
[coordinates of x- intercept (given)
Moreover note that if 2 lines are perpendicular, the product of their slope is always equal to (- 1) [ or the reciprocal inverse]
So the function of such a line is y = (4/3).x + b {4/3 and -3/4 are reciprocal inverse),
As before, we have to find b, knowing y passes through C(6, 0 )
y=4/3.x + b; 0 = 4/3(6) + b and b= -8
At last the equation that is perpendicular to the graph is : y=(4/3).x -8
I think there is an error in the answers given by the problem