Line m passes through the points (5, 1) and (8, 6) while line n passes through the points (-4, 3) and (-1, 8). Which statement accurately describes the relationship between the two lines?

Question

Line m passes through the points (5, 1) and (8, 6) while line n passes through the points (-4, 3) and (-1, 8).  Which statement accurately describes the relationship between the two lines?

Mercury · Answer

choices:

A. Lines m and n have the same slope so they are perpendicular.
 B. Lines m and n have opposite reciprocal slopes so they are perpendicular. 
C. Lines m and n have opposite reciprocal slopes so they are parallel. 
D. Lines m and n have the same slope so they are parallel.

in order to figure this out, we'll need to calculate the slope of both lines m and n.

for line m, let one of the points be (x1,y1) and the other point be (x2,y2) then calculate slope with the formula

$$m = \frac{ y_{2}-y_{1} }{ x_{2}-x_{1} }$$

repeat this process with line n

if the slopes are equal, then they're parallel
if the slopes are opposite reciprocals (i.e. 1/a and -a) then the lines are perpendicular