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BECE Mathematics 2022 Paper

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Question : 11

Total: 40

Given that

P(3,-2)

Q(-2,4)

are points in a plane, find the gradient of the line joining

P

Q

$-\frac{6}{5}$
$\frac{6}{5}$
$\frac{5}{6}$
$\;\; -\frac{5}{6}$

Solution:

Concept:

The gradient of a line is the ratio of the change in

y

to the change in

x

between two points.

Explanation:

For points

P(3,-2)

and

Q(-2,4)

, use the formula:

\text{Gradient} = \frac{y_2 - y_1}{x_2 - x_1}

Here,

x_1 = 3

,

y_1 = -2

,

x_2 = -2

, and

y_2 = 4

.

Substitute the values:

\text{Gradient} = \frac{4 - (-2)}{-2 - 3} = \frac{4 + 2}{-5} = \frac{6}{-5} = -\frac{6}{5}

Answer:

-\frac{6}{5}

This is Option A.

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