JAMB Mathematics 2021 Paper

Concept:Parallel lines always have equal slopes. Find the slope of the given line and set it equal to the slope from the two given points.Explanation:Start with the equation $2y + 8x - 17 = 0$.Rearrange to the form $y = mx + c$:$2y = -8x + 17$$y = -4x + \frac{17}{2}$Therefore, the slope of the given line is $-4$.For parallel lines, the slope of the unknown line must also be $-4$.Use the slope formula for $(-1, -p)$ and $(-2, 2)$:$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-p)}{-2 - (-1)}$Simplify the numerator and denominator:$-4 = \frac{2 + p}{-2 + 1} = \frac{2 + p}{-1}$$-4 = -(2 + p)$$-4 = -2 - p$Add $2$ to both sides: $-2 = -p$Thus, $p = 2$.Answer:$p = 2$The correct option is D.