JAMB Mathematics 2011 Paper

Concept:Two lines are perpendicular when the product of their slopes is $-1$.Use the slope of the given line to obtain the perpendicular slope, then apply the given point.Explanation:Start with the given line: $2y = 5x + 4$.Divide through by $2$ to get $y = \dfrac{5}{2}x + 2$.The slope of this line is $m_1 = \dfrac{5}{2}$.For perpendicular lines, $m_1 \times m_2 = -1$.Therefore, $m_2 = -\dfrac{1}{m_1} = -\dfrac{1}{5/2} = -\dfrac{2}{5}$.The required line passes through $(4, 2)$ with slope $-\dfrac{2}{5}$.Using $y - y_1 = m(x - x_1)$: $y - 2 = -\dfrac{2}{5}(x - 4)$.Simplify: $y - 2 = -\dfrac{2}{5}x + \dfrac{8}{5}$.Add $2$ to both sides: $y = -\dfrac{2}{5}x + \dfrac{18}{5}$.Multiply every term by $5$: $5y = -2x + 18$.Rearrange to standard form: $5y + 2x - 18 = 0$.Answer:The equation of the perpendicular line is $5y + 2x - 18 = 0$, which is option B.