Question

Find the equation of a line whose gradient $$= \sqrt{3}$$ and $$y$$-intercept $$= \frac{-2}{3}$$.

Answer 1

The equation of a line with slope $$m$$ and $$y$$-intercept $$c$$ is given by $$y = mx + c$$.

Here, $$m = \sqrt{3}$$ and $$c = -\frac{2}{3}$$:

$$y = \sqrt{3}x - \frac{2}{3}$$ 

Multiplying both sides by $$3$$: 

$$3y = 3\sqrt{3}x - 2$$ 

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