Answer:
- parallel: y +4 = -4(x +6)
- perpendicular: y -4 = 1/4(x +6)
Step-by-step explanation:
You want the equations of the lines parallel and perpendicular to y=-4x+4 through the points (-6, -4) and (-6, 4), respectively.
Slope relations
The equation of the given line is in slope-intercept form. This means its slope is the coefficient of x: -4.
Parallel lines have the same slope, so the parallel line will have slope -4.
Perpendicular lines have opposite reciprocal slopes, so the perpendicular line will have slope -1/(-4) = 1/4.
Point-slope equation
The point-slope equation of a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
This problem gives you a point on each line, and we know the required slope, so this form of the equation for a line is just what we need.
Parallel line
m = -4, (h, k) = (-6, -4)
y +4 = -4(x +6)
Perpendicular line
m = 1/4, (h, k) = (-6, 4)
y -4 = 1/4(x +6)
