WAEC 2024 Mathematics · Question 25

The gradient of the line joining the points P(2, -8) and Q(1, y) is -4. Find the value of y

Options

A.2
B.4
C.-4
D.-3

Answer: C. -4

Explanation written with AI and checked against the answer key

Analyze the question: We are given two points, P(2, -8) and Q(1, y), and the gradient (slope) of the line through them is -4. We need to find y. Concept: The gradient of a line through (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁) / (x₂ - x₁) Solution: Let P = (2, -8) and Q = (1, y). m = (y - (-8)) / (1 - 2) -4 = (y + 8) / (-1) Multiply both sides by -1: 4 = y + 8 y = 4 - 8 = -4 Check: Gradient = (-4 + 8)/(1 - 2) = 4/(-1) = -4 ✓ Answer: y = -4, which is option C. Tip: Always subtract the coordinates in the same order on the top and bottom (y₂ - y₁ over x₂ - x₁). Mixing the order is the most common cause of sign errors. Always substitute your answer back to confirm it gives the stated gradient.

AI can make mistakes. Report anything that looks wrong.