Question

Find the equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.

Answer 1

It is given that the lines are equally inclined to the axes.
So, their inclinations with the positive x-axis are ${45}^{\circ }\mathrm{and}{135}^{\circ }$.
Let $m_1\mathrm{and}{m}_2$ be the slopes of the lines.

$\therefore m_1=\tan {45}^{\circ }=1\mathrm{and}{m}_2=\tan {135}^{\circ }=-\tan {45}^{\circ }=-1$

Thus, the equations of the lines passing through (0, 5) with slopes $1\mathrm{and}-1$ are

$$\begin{gathered} y-5=1\left(x-0\right)\mathrm{and}y-5=-1\left(x-0\right) \\ \Rightarrow y-x-5=\mathrm{and}y+x-5=0 \\ \Rightarrow y=x+5\mathrm{and}x+y=5 \end{gathered}$$