Answer:
C. y -6 = -4(x -(-2))
Step-by-step explanation:
You want the equation of the line XY through point (-2, 6) that is perpendicular to the line y = 1/4x +4.
The slope of the given line is the coefficient of x, 1/4.
The slope of the perpendicular line will be the opposite reciprocal of this:
m = -1/(1/4) = -4
The equation of a line with slope m through point (h, k) can be written as ...
y -k = m(x -h)
We want the line with slope -4 through point (-2, 6), so its equation is ...
y -6 = -4(x -(-2)) . . . . . . matches choice C