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WAEC 2016 Mathematics · Question 12

A straight line passes through the points P(1,2) and Q(5,8). Calculate the gradient of the line PQ

Options

  1. A.35\frac{3}{5}
  2. B.23\frac{2}{3}
  3. C.32\frac{3}{2}
  4. D.53\frac{5}{3}

Answer: C. 32\frac{3}{2}

Explanation written with AI and checked against the answer key

Analyze the question: We need the gradient (slope) of the line through P(1, 2) and Q(5, 8).

Concept: The gradient measures how steep a line is:

m=y2−y1x2−x1=change in ychange in xm = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\text{change in } y}{\text{change in } x}

Solution:

Let P(1, 2) = (x₁, y₁) and Q(5, 8) = (x₂, y₂).

m=8−25−1=64=32m = \frac{8 - 2}{5 - 1} = \frac{6}{4} = \frac{3}{2}

Check: Swapping the order of the points gives (2 − 8)/(1 − 5) = (−6)/(−4) = 3/2, the same result.

Answer: C. 3/2

Tip: Always subtract the y-values and the x-values in the same order. Mixing the order (for example 8 − 2 over 1 − 5) gives the wrong sign. Also remember that "rise over run" puts the y-change on top. Option A (3/5) and option D (5/3) are tempting traps for students who mix up the numbers.

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