BECE Mathematics 2024 Paper

Concept:The equation of a straight line is $y = mx + c$, where $m$ is the slope and $c$ is the $y$-intercept.Explanation:From the graph, the line passes through the points $(1,1)$ and $(0,3)$.The slope is calculated as $m = \frac{y_2 - y_1}{x_2 - x_1}$.Using $(x_1,y_1) = (1,1)$ and $(x_2,y_2) = (0,3)$:$m = \frac{3 - 1}{0 - 1} = \frac{2}{-1} = -2$.Now use the general point $(x,y)$ and a known point, say $(1,1)$:$\frac{y - 1}{x - 1} = -2$.Rewrite $-2$ as $\frac{-2}{1}$, then cross multiply:$y - 1 = -2(x - 1)$.Simplify: $y - 1 = -2x + 2$.Add $1$ to both sides: $y = -2x + 3$.This matches the line's $y$-intercept of $3$, confirming the equation.Answer:$y = -2x + 3$, which is Option A.