WAEC 2018 Mathematics · Question 31

The equation of the line through the points (4,2) and (-8, -2) is 3y = px + q, where p and q are constants. Find the value of p.

Options

Answer: A. 1

Explanation written with AI and checked against the answer key

Analyze the question: We need the equation of the line through (4, 2) and (-8, -2), written in the form 3y = px + q, and then read off p. Concept: The gradient (slope) of a line through two points is m = (y₂ − y₁) / (x₂ − x₁) If 3y = px + q, then y = (p/3)x + q/3, so the gradient is p/3. Solution: Step 1: Find the gradient. m = (−2 − 2) / (−8 − 4) = (−4) / (−12) = 1/3 Step 2: Equate to p/3. p/3 = 1/3, so p = 1 Step 3: Find q as a check, using the point (4, 2). 3(2) = 1(4) + q, so 6 = 4 + q, giving q = 2 The line is 3y = x + 2. Check with (−8, −2): 3(−2) = −6 and −8 + 2 = −6 ✓. Answer: p = 1, which is option A. Tip: When a line is given as 3y = px + q, divide by 3 to get the gradient p/3 and compare it with the gradient you calculated from the two points. Always check with the second point to be sure.

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