Answer:
The slope of the line that is perpendicular to y = 4x + 6 is the negative reciprocal of the slope of y = 4x + 6, which is -1/4.
We can use the point-slope form of a line, y - y1 = m(x - x1), to find the equation of the line that passes through the point (8, -4) and has a slope of -1/4, where m = -1/4 and (x1, y1) = (8, -4).
Plugging in the values, we get:
y - (-4) = -1/4 (x - 8)
y + 4 = -1/4 x + 2
Multiplying both sides by 4, we get:
4y + 16 = -x + 8
Adding x to both sides, we get:
4y + 16 + x = 8
y = -x/4 - 2
So the equation of the line that is perpendicular to y = 4x + 6 and passes through the point (8, -4) is y = -x/4 - 2.