JAMB 2011 · UTME · Q33

Coordinate geometry

Find the equation of a line perpendicular to the line $2y = 5x + 4$ which passes through $(4, 2)$ .

Worked solution (try it first)

$2y = 5x + 4$ gives $y = \frac52x + 2$ , so its gradient is $\frac52$ .
The perpendicular gradient is the negative reciprocal, $-\frac25$ .
Through $(4, 2)$ : $y - 2 = -\frac25(x - 4)$ .
Multiply by 5: $5y - 10 = -2x + 8$ .
Collect terms: $5y + 2x - 18 = 0$ , option B.

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