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 line?

Answer 1

They both have a slope of 5/3, which means they are parallel.

Answer 2

(5,1)(8,6)
slope = (6-1) / (8-5) = 5/3

y = mx + b
slope(m) = 5/3
(5,1)
y = mx + b
1 = 5/3(5) + b
1 = 3 + b
1 - 3 = b
-2 = b
equation for line m : y = 5/3x - 2

(-4,3)(-1,8)
slope = (8-3) / (-1 - (-4) = 5/3

y = mx + b
slope(m) = 5/3
(-4,3)
y = mx + b
3 = -4(5/3) + b
3 = -20/3 + b
3 + 20/3 = b
9/3 + 20/3 = b
29/3 = b
equation of line n : y = 5/3x + 29/3

the relationship between the two lines is that they are parallel lines (same slope but different y intercepts)