Question

Find the equation of the line whose angle of inclination and y-intercept are given $\theta ={45}^o$, intercept is $3$.

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 $\theta ={45}^0$, therefore,

$m=\tan {45}^0=1$

Thus, the slope of the line is $1$.

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 $m=1$ and y-intercept $c=3$, the equation of a line is:

$y=mx+c\Rightarrow y=(1\times x)+3\Rightarrow y=x+3\Rightarrow x-y+3=0$

Hence, the equation of a line is $x-y+3=0$.