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)?

Sep 30, 2014

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 .

${m}_{a} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{4 - 6}{- 1 - 2} = \frac{- 2}{-} 3 = \frac{2}{3}$

${m}_{b} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 3 - 1}{2 - 8} = \frac{- 4}{-} 6 = \frac{- 2}{-} 3 = \frac{2}{3}$

The slopes are equal so the lines are parallel.