Find the equation of the straight line passing through (–2, 4) and making non-zero inter-cepts whose sum is zero.

The eq’n of the st.line making non-zero intercepts is $\frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1 ...\left(1\right)$
Intercepts on x – axis is a and y – axis is b
Given intercepts whose sum is zero
$\text{ i.e., }\mathrm{a}+\mathrm{b}=0\Rightarrow \mathrm{a}=-\mathrm{b}$
Sub. in (1) $\frac{\mathrm{x}}{-\mathrm{b}}+\frac{\mathrm{y}}{\mathrm{b}}=1\Rightarrow -\mathrm{x}+\mathrm{y}=\mathrm{b}$
Passing through (–2, 4)

 $\therefore \mathrm{b}=6$
$\therefore \text{ eq'n of st.line is }-\mathrm{x}+\mathrm{y}=6\Rightarrow \mathrm{x}-\mathrm{y}+6=0$