JAMB 2001 · UME · Q28

Coordinate geometry

A straight line makes an angle of $30^\circ$ with the positive $x$ -axis and cuts the $y$ -axis at $y = 5$ . Find the equation of the straight line.

Worked solution (try it first)

The gradient is the tangent of the angle: $\tan 30^\circ = \frac{1}{\sqrt3}$ .
The $y$ -intercept is 5, so $y = \frac{1}{\sqrt3}x + 5$ .
Multiply every term by $\sqrt3$ : $\sqrt3y = x + 5\sqrt3$ , option A.

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