Question

From differential equation representing the family of lines making equal intercepts on the co-ordinate axes.

Answer 1

Equation of line by intercept form-

$\frac{x}{a}+\frac{y}{b}=1$

Whereas,

$a=x$-intercept

$b=y$-intercept

Given:- $a=b\left(\text{Equal intercept}\right)$

Therefore, equation of line is-

$x+y=a$

Differentiating above equation, we get

$dx+dy=0$

$\Rightarrow \frac{dy}{dx}=-1$