Question

Find the equation of a line whose inclination is $$30^{\circ}$$ and whose $$y$$-intercept is –2.

Answer 1

The slope of the line is $$m = \tan 30^{\circ} = \frac{1}{\sqrt{3}}$$

The $$y$$-intercept is $$c = -2$$

Using the slope-intercept form of the equation of a line, $$y = mx + c$$: $$y = \frac{1}{\sqrt{3}}x - 2$$

Multiplying both sides by $$\sqrt{3}$$:

$$\sqrt{3}y = x - 2\sqrt{3}$$

$$x - \sqrt{3}y - 2\sqrt{3} = 0$$

Thus, the required equation is $$x - \sqrt{3}y - 2\sqrt{3} = 0$$.