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? 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.

Answer 1

Find the equations of the lines...

First find the slope...(y2-y1)/(x2-x1)=m

m=(6-1)/(8-5)=5/3 and it passes through (5,1) so

y=mx+b becomes:

y=5x/3+b and using (5,1)

1=5(5)/3+b

1=25/3+b

3/3-25/3=b

b=-22/3 so 

y1=(5x-22)/3

.... now y2...

m=(8-3)/(-1--4)=5/3 (note it has the same slope as y1...

y=5x/3+b and using the point (-1,8)

8=5(-1)/3+b

8=-5/3+b

24/3+5/3=b

b=29/3, now note that the y-intercept is different...

y2=(5x+29)/3

Since these lines have the same slope but different y-intercepts, they are parallel to each other. (and will never intersect.)