Answer:
y = 4/3(x) - 8
Explanation:
First we have to find the equation for the given line (I use y = mx + b for everything, although I think it can be done with other formats). The equation for slope is (y2 - y1)/(x2 - x1) = m, so we'll start with that.
(-2 - 4) / (4 - (-4)) = m
-6 / 8 = m
m = -3/4
Now, let's find the rest of the equation. We can do this by treating b as the unknown variable it is, and plugging in a known xy pair, then simply solving for the unknown variable.
y = mx + b; y = 4, x = -4, m = -3/4
4 = -4(-3/4) + b
4 = 3 + b
b = 1
Now we have the original line's equation, y = -3/4(x) + 1. We need to find the new line's slope by finding the negative reciprocal of the base line's. For that, we simply flip the numerator and denominator, then multiply it by -1, to get 4/3. Now we find b again, using the point (6, 0).
y = mx + b; y = 0, x = 6, m = 4/3
0 = 4/3(6) + b
0 = 8 + b
b = -8
This makes our final answer y = 4/3(x) - 8.