Find (a) the equation of a line that is parallel to the given line and includes the given point, and (b) the equation of a line that is perpendicular to the given line through the given point. Write both answers in slope-intercept form.

Question

y = -4x + 2, (5, 4)

Answer 1

(a) You want a line with slope -4 that passes through (5,4)
The equation will have the form
y = -4x + b
Now substityute x = 5 and y = 4 and solve for b.
4 = -20 + b
b = 24
y = -4x + 24

(b) You want a line with slope 1/4 that passes through (5,4)
Follow the same procedure:
y = x/4 + b'
Let x = 5, y = 4 and solve for b'
4 = 5/4 + b'
b' = 11/4
y = (x/4) + 11/4