Question

Suppose we are given the following information.

Line 1 passes through (0, 6) and (6, 4).

Line 2 passes through (-1, -7) and (1, -1).

Are these lines parallel, perpendicular, or neither?

1. Since the product of the slope is -1, hence the lines are perpendicular

### Parallel and Perpendicular lines

Two lines are known to be parallel if they have the same slope while if two lines are perpendicular if the product of the slope is -1
Given the coordinates of line 1 passing through (0, 6) and (6, 4), the slope is given as;
Slope = 4-6/6-0
Slope = -2/6
Slope = -1/3
Similarly for the coordinate points (-1, -7) and (1, -1).
Slope = -1+7/1+1
Slope of line 2 = 6/2
Slope = 3
Take the product of the slopes
Slope = -1/3 * 3
slope = -1
Since the product of the slope is -1, hence the lines are perpendicular