Question

Find the equation of the lines which cut off from the axes equal intercepts?

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that},\mathrm{equation}\mathrm{of}\mathrm{a}\mathrm{straight}\mathrm{line}\mathrm{in}\mathrm{intercept}\mathrm{form}\mathrm{is}, \\ \frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1...\left(1\right) \\ \mathrm{where}\mathrm{a}=\mathrm{x}-\mathrm{intercept};\mathrm{b}=\mathrm{y}-\mathrm{intercept} \\ \mathrm{Now},\mathrm{a}=\mathrm{b} \\ \mathrm{Put}\mathrm{a}=\mathrm{b}\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ \frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{a}}=1 \\ \Rightarrow \mathrm{x}+\mathrm{y}=\mathrm{a} \end{gathered}$$