parallel, perpendicular, or neither?

Question

Are the lines given by y = –2x + 3 and 6y – 3x = –18 parallel, perpendicular, or neither?

Answer 1

Lines are parallel if they have the same slope and different y-intercepts.

Lines are perpendicular if their slopes are negative reciprocals of each other.

The first equation is in slope intercept form, y = mx + b. Its slope is -2 and the y-intercept is (0, 3)

You need to write the second equation, 6y-3x=-18 in slope intercept form in order to be able to determine if the lines are parallel, perpendicular or neither.

6y -3x = -18

+3x +3x

6y = 3x -18

6y/6 = 3/6 x - 18/6

y = 1/2 x - 3; slope is 1/2 and y-intercept is (0, -3)

Since the slopes are negative reciprocals of each other, -2 and 1/2, then these lines are perpendicular.