Is The Line through points P(0, 5) and Q(-1, 8) parallel to the line through points R(3, 3) and S(5, -1)? Explain.

Question

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Answer 1

line through P(0, 5) and Q(-1, 8):

slope = m = (y₂ - y₁) / (x₂ - x₁) = (8 - 5) / (-1 - 0) = 3 / -1 = -3

line through R(3, 3) and S(5, -1):

slope = m = (y₂ - y₁) / (x₂ - x₁) = (-1 - 3) / (5 - 3) = -4 / 2 = -2

Parallel lines have equal slopes. Since the two lines have different slopes, they are not parallel.

Answer 2

PQ slope is (8-3)/(-1-0) = -5

RS slope is (3--1)(3-5) = 4/-2= -2

slopes are different, so they aren't parallel

slope = the difference in y-coordinates divided by difference in x - coordinates ("rise over run") the vertical change in 2 points divided by the horizonal change.