BECE Mathematics 2023 Paper

Concept:The gradient of a straight line measures its steepness and is found by dividing the change in $y$ by the change in $x$ between two given points.Explanation:Let $P(-5,-3)$ be the point $(x_1, y_1)$ and $Q(-4,-7)$ be the point $(x_2, y_2)$.Thus, $x_1 = -5$, $y_1 = -3$, $x_2 = -4$, and $y_2 = -7$.The formula for gradient is:$$\text{Gradient} = \frac{y_2 - y_1}{x_2 - x_1}$$Substitute the given coordinates into the formula:$$\text{Gradient} = \frac{-7 - (-3)}{-4 - (-5)}$$Simplify the numerator and the denominator separately:$$-7 - (-3) = -7 + 3 = -4$$$$-4 - (-5) = -4 + 5 = 1$$Therefore:$$\text{Gradient} = \frac{-4}{1} = -4$$The line $PQ$ falls from left to right, so the negative gradient confirms that the line slopes downward.Answer:$$\boxed{-4}$$The correct choice is A. $-4$.