BECE Mathematics 2023 Paper

Concept:The mapping shows a constant decrease in $y$ as $x$ increases by $1$.So the rule is a linear equation of the form $y = mx + c$.Explanation:For each step in $x$, the $y$-values are: $4, 2, 0, -2, -4$.The difference between consecutive $y$-values is $-2$, so the slope is $m = -2$.Use the first pair $(x=1, y=4)$ in $y = mx + c$.Substitute $m=-2$, $x=1$, and $y=4$: $4 = -2(1) + c$.Simplify: $4 = -2 + c$, so $c = 4 + 2 = 6$.Hence the rule is $y = -2x + 6$.Check: for $x=2$, $y = -2(2)+6 = 2$; for $x=3$, $y=0$.This matches the given mapping exactly.Answer:$y = -2x + 6$ (Option D).