Is the line through points p(3, -5) and q(1, 4) parallel to the line through points r(-1, 1) and s(3, -3)? explain. a. yes; the lines have equal slopes. b. no; the lines have unequal slopes. c. no; one line has zero slope, the other has no slope. d. yes; the lines are both vertical.

b. No; the lines have unequal slopes.

Step-by-step explanation:

To determine whether the lines are parallel or not we have to compare their slopes. Provided we have 2 points (x₁, y₁) and (x₂, y₂), we can calculate the slope (m) using the following expression:

m = y₂ - y₁ / x₂ - x₁

Line A goes through points P(3, -5) and Q(1, 4). Its slope is:

mA = 4 - (-5) / 1 - 3 = -9/2

Line B goes through points R(-1, 1) and S(3, -3). Its slope is:

mB = -3 - 1/3 - ( -1) = -1

Since mA ≠ mB, the linea are not parallel.

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step-by-step explanation: