Question

Are the following lines parallel, perpendicular, or neither?

y = 3(x + 7)

y + 5 = -1/3x

O parallel
O perpendicular
O neither

Answer 1

perpendicular

Explanation:

Find the slope for both lines and compare. Same slope would mean parallel. Different slopes means intersecting lines. But specifically if the slopes are opposite sign and reciprocals (one is flipped over from the other) then they are perpendicular.

Put them in slope-intercept form to find the slope.

y = mx + b

m is the slope (number by the x)

y = 3(x+7)

distribute the 3.

y = 3x + 21

This line has a slope of 3.

y + 5 = -1/3 x

y = -1/3 x - 5

This line has a slope of -1/3.

-1/3 and 3 are negative reciprocals. They have opposite signs. Also 1/3 is just 3 but flipped over. They are perpendicular.