WAEC 2017 Mathematics · Question 14

Calculate the gradient (slope) of the joining points (-1, 1) and (2, -2)

Options

A.-1
B. $\frac{-1}{2}$
C. $\frac{1}{2}$
D.1

Answer: A. -1

Explanation written with AI and checked against the answer key

Analyze the question: We need the gradient of the line passing through (-1, 1) and (2, -2).

Concept: The gradient (slope) between two points (x₁, y₁) and (x₂, y₂) is:

m = \frac{y_2 - y_1}{x_2 - x_1}

Solution:

Let (x₁, y₁) = (-1, 1) and (x₂, y₂) = (2, -2).

m = \frac{-2 - 1}{2 - (-1)} = \frac{-3}{2 + 1} = \frac{-3}{3} = -1

Check: Swapping the points gives the same result: (1 - (-2)) / (-1 - 2) = 3 / (-3) = -1. ✓

The negative gradient makes sense: as x increases from -1 to 2, y falls from 1 to -2, so the line slopes downward.

Answer: A. -1

Exam tip: Be careful with double negatives. The most common mistake is writing 2 - 1 instead of 2 - (-1) in the denominator, which would wrongly give -3. Always put brackets around negative coordinates. Also, keep the order consistent: if y₂ is on top, x₂ must come first in the bottom.

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