Answer:
9x -4y = -44
Step-by-step explanation:
You want the equation of the line through (-4, 2) and perpendicular to the line through (-4, 6) and (5, 2).
The equation of a line through (h, k) and perpendicular to the line through (x1, y1) and (x2, y2) can be written as ...
(x2 -x1)(x -h) +(y2 -y1)(y -k) = 0
Using the given points, this becomes ...
(5 -(-4))(x -(-4)) +(2 -6)(y -2) = 0
9(x +4) -4(y -2) = 0
Expanding this gives the general form equation:
9x -4y +44 = 0
Subtracting the constant gives the standard form equation:
9x -4y = -44
