WAEC Mathematics 2015 Paper

Concept:The gradient of a straight line is calculated using two known points: $m = \frac{y_2 - y_1}{x_2 - x_1}$.Explanation:From the table, take the first two complete points. Point 1: $(x_1, y_1) = (0, 3)$ Point 2: $(x_2, y_2) = \left(1\frac{1}{4}, 5\frac{1}{2}\right)$ Convert to improper fractions: $x_2 = \frac{5}{4}$, $y_2 = \frac{11}{2}$ Substitute into the gradient formula: $m = \frac{\frac{11}{2} - 3}{\frac{5}{4} - 0}$ Simplify the numerator: $\frac{11}{2} - 3 = \frac{11 - 6}{2} = \frac{5}{2}$ So: $m = \frac{\frac{5}{2}}{\frac{5}{4}} = \frac{5}{2} \times \frac{4}{5}$ This gives: $m = 2$ Since the table is for a linear graph, any other pair of complete points would give the same gradient.Answer:The gradient of the line is $2$. Correct option: B