WAEC 2022 Mathematics · Question 27

The straight line y = mx - 4 passes through the point(-4,16). Calculate the gradient of the line

Options

A.-5
B.-3
C.3
D.5

Answer: A. -5

Explanation written with AI and checked against the answer key

Analyze the question: The line y = mx - 4 passes through (-4, 16). The point lies on the line, so its coordinates must satisfy the equation. We need to find m, the gradient. Concept: If a point lies on a line, substitute its x and y values into the equation of the line. Solution: Substitute x = -4 and y = 16 into y = mx - 4: 16 = m(-4) - 4 16 = -4m - 4 Add 4 to both sides: 20 = -4m Divide both sides by -4: m = -5 Check: y = -5x - 4. When x = -4, y = -5(-4) - 4 = 20 - 4 = 16 ✓ Tip: For "passes through a point" questions, always substitute the point's coordinates into the equation and solve for the unknown. Watch your signs carefully: a negative x-value multiplied by m is where most students slip. Always check by plugging your answer back in.

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