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.)
