$\text{ Equation of line which makes equal angles with axes and passing through the origin is }$

$\text{ A line makes equal angles with axes, means it makes an angle }{45}^{\circ }\text{ with }x\text{-axis in the }$$\text{ positive direction. }$

$\text{ Equation of the line passing through the point }\left(x_1,y_1\right)\text{ and having slope }m\text{ is }$$y-y_1=m\left(x-x_1\right)$

$\text{ Here }m=\tan \theta ,\text{ where }\theta \text{ is the angle made by the line with }x-\text{ axis in the positive Direction}$

$\text{ Hence the slope of the line is }m=\tan \left({45}^{\circ }\right)=1$

$\text{ The equation of the line passing through the point }(0,0)\text{ and having slope }1\text{ is }$

$\begin{array}{c}y-0=1\left(x-0\right)\\ y=x\\ x-y=0\end{array}$

$\text{ Therefore, the equation of the line is }x-y=0$