WAEC 2023 Mathematics · Question 43

Find the gradient of the line passing through the points $(\frac{1}{2}, \frac{- 1}{3}) and ( 3 , \frac{2}{3})$

Options

A. $\frac{2}{5}$
B. $\frac{5}{2}$
C. $\frac{2}{7}$
D. $\frac{7}{2}$

Answer: A. $\frac{2}{5}$

Explanation written with AI and checked against the answer key

Analyze the question: We need the gradient (slope) of the line through two given points. Concept: Gradient m = (y₂ − y₁) / (x₂ − x₁) Solution: Points: (x₁, y₁) = (1/2, −1/3) and (x₂, y₂) = (3, 2/3) Change in y: 2/3 − (−1/3) = 2/3 + 1/3 = 1 Change in x: 3 − 1/2 = 6/2 − 1/2 = 5/2 Gradient: m = 1 ÷ (5/2) = 1 × 2/5 = 2/5 My working agrees. Answer: A. 2/5 Tip: With fractions, find the rise and the run separately first, then divide. Dividing by a fraction means multiplying by its reciprocal. Also, keep the points in the same order in both the numerator and denominator. Swapping the order in only one of them gives the wrong sign.

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Find the gradient of the line passing through the points (12, −13) and (3,23)(\frac{1}{2}, \frac{- 1}{3}) and ( 3 , \frac{2}{3})(21​, 3−1​) and (3,32​)

Options

Answer: A. 25\frac{2}{5}52​

Find the gradient of the line passing through the points $(\frac{1}{2}, \frac{- 1}{3}) and ( 3 , \frac{2}{3})$

Answer: A. $\frac{2}{5}$