JAMB Mathematics 2023 Paper

Concept:A straight line has the same gradient at every point, so any two points on the line give the same slope.Explanation:Start with the line $3y+6x=48$.Divide through by $3$: $y+2x=16$.Rewrite as $y=-2x+16$.Therefore, the gradient is $m=-2$.For points $A(-2,k)$ and $B(4,8)$, the gradient is $\frac{8-k}{4-(-2)}$.Simplify: $4-(-2)=6$.So $m=\frac{8-k}{6}$.Since the line passes through both points, $\frac{8-k}{6}=-2$.Multiply both sides by $6$: $8-k=-12$.Solve for $k$: $k=8+12$.Thus, $k=20$.Answer:$k=20$, which is option B.