Given: Line PQ contains points (w, v) and (x, z) and line P'Q' contains points (w + a, v + b) and (x + a, z + b). Lines PQ and P'Q' are parallel. Prove: Parallel lines have the same slope. On a coordinate plane, 2 lines are shown. Line Q P goes through (w, v) and (x, z). Line Q prime P prime goes through (w + a, v + b) and (x + a, z + b). Since slope is calculated using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction, the slope of both lines is equivalent to . It is given that the lines are parallel, and we calculated that the slopes are the same. Therefore, parallel lines have the same slopes. StartFraction v minus z Over w minus x EndFraction StartFraction w minus x Over v minus Z EndFraction StartFraction v minus z + b Over x minus z + a EndFraction StartFraction w minus x + a Over v minus z + b EndFraction