Question

How do you determine if the two lines are parallel, perpendicular, or neither if line a passes through points (–1, 4) and (2, 6) and line b passes through points (2, –3) and (8, 1)?

Answer 1

First we need to find the slopes of the lines to make any determinations.

If the slopes are equal then the lines are parallel .
If the slopes are negative reciprocals then the lines are perpendicular .
If the slopes are neither of the above are true then the lines are neither .

`m_(a)=(y_2-y_1)/(x_2-x_1)=(4-6)/(-1-2)=(-2)/-3=2/3`

`m_(b)=(y_2-y_1)/(x_2-x_1)=(-3-1)/(2-8)=(-4)/-6=(-2)/-3=2/3`

The slopes are equal so the lines are parallel.