JAMB 1997 · UME · Q33

Coordinate geometry

The angle between the positive horizontal axis and a given line is $135^\circ$ . Find the equation of the line if it passes through the point $(2, 3)$ .

Worked solution (try it first)

The gradient is the tangent of the angle with the positive $x$ -axis: $\tan 135^\circ = -1$ .
Through $(2, 3)$ : $y - 3 = -1(x - 2)$ , so $y - 3 = -x + 2$ .
Add $x$ and 3 to both sides: $x + y = 5$ , option C.

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