Question

Parallel and Perpendicular Lines:


1. Write the equation of the line which passes though (-4, 2) and is parallel to y = -x + 6 in slop-intercept form.

2. Write the equation of the line which passes though (2, -3) and is perpendicular to y = 4x + 7 in slope-intercept form.

Answer 1

1. If you are looking for a parallel line, the slope will be the same. So, in this case, the slope is -1.
y - y1 = m(x - x1) using slope(m) - 1 and points (-4,2)
y - 2 = -1(x - (-4)
y - 2 = -1(x + 4)
y - 2 = -x - 4
y = -x - 4 + 2
y = -x - 2 <-- this is it :)

2. If you are looking for perpendicular, the slope will be the negative reciprocal. So, in this case, the slope is -1/4.
y - y1 = m(x - x1) using slope -1/4 and points (2,-3)
y - (-3) = -1/4(x - 2)
y + 3 = -1/4x + 2/4
y = -1/4x + 2/4 - 3
y = -1/4x + 2/4 - 12/4
y = -1/4x - 10/4
y = -1/4x - 5/2 <-- this is it :)

Answer 2

eq. of line parallel to y=-x+6 is
y=-x+c
because it passes through (-4,2)
2=-(-4)+c
2=4+c
c=2-4=-2
reqd. eq is
y=-x-2
or x+y+2=0

Answer 3

slope form is y=-x-2