Question

Find the equation of the line whose angles of inclination and y-intercept are given $\theta ={60}^o$, y-intercept is $-2$.

Answer 1

We know that if $\theta$ is the inclination of a straight line, then $\tan \theta$ is called the slope (or gradient) of a line. The slope of a line is usually denoted by $m$.

Here, it is given that $\theta ={60}^0$, therefore,

$m=\tan {60}^0=\sqrt{3}$

Thus, the slope of the line is $\sqrt{3}$.

We also know that the equation of a line is $y=mx+c$ where $m$ is the slope of the line and $c$ is the y-intercept.

Therefore, with slope $m=\sqrt{3}$ and y-intercept $c=-2$, the equation of a line is:

$y=mx+c\Rightarrow y=\sqrt{3}x+(-2)\Rightarrow y=\sqrt{3}x-2\Rightarrow \sqrt{3}x-y-2=0$

Hence, the equation of a line is $\sqrt{3}x-y-2=0$.