Question

Find the equation of line cutting an intercept at $-2$ on the $y-$ axis and equally inclined to the axes

Answer 1

Given $y-$intercept$\left(c\right)=-2$ and the line is equally inclined to the axis i.e., same angle to the x-axis and y-axis(say)$=\theta$

but the angle between the axes is ${90}^{\circ }$

$2\theta ={90}^{\circ }\Rightarrow \theta ={45}^{\circ }$

As slope and $y-$intercept are given.

Equation of line is $y=mx+c$

$c=-2$ and $m=\tan {45}^{\circ }$ as line is equally inclined to the axes.

$c=-2$ and $m=1$

Equation of line is $y=x-2$