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WAEC Mathematics 2023 Paper

Question : 45

Total: 50

\left(\frac{1}{2}, -\frac{1}{3}\right) \text{ and } \left(3, \frac{2}{3}\right)

Solution:

Concept:

The gradient of a line through two points is the change in

y

divided by the change in

x

Explanation:

Let the points be

\left(\frac{1}{2}, -\frac{1}{3}\right)

and

\left(3, \frac{2}{3}\right)

Use the gradient formula:

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

Substitute the coordinates:

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

Simplify the numerator:

\frac{2}{3} + \frac{1}{3} = 1

Simplify the denominator:

3 - \frac{1}{2} = \frac{5}{2}

So,

m = 1 \div \frac{5}{2} = 1 \times \frac{2}{5} = \frac{2}{5}

Answer:

The gradient is

\frac{2}{5}

, which is Option A.

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