Question

Find the equation of the line passing through the point $(2,-5)$ and making an intercept of $-3$ on the y-axis.

Answer 1

Let the equation be $\frac{x}{a}+\frac{y}{b}=1$

$\because$ Give $-3$ is the intercept on the y-axis

then $\frac{x}{a}+\frac{y}{-3}=1$

Now, it passes through $(2,-5)$

$\therefore \frac{2}{a}+\frac{5}{3}=1$

$6+5a=3a$

$\Rightarrow 6=-2a$

$\Rightarrow a=-3$

$\therefore$ Required line: $\frac{x}{-3}+\frac{y}{-3}=1$

$\Rightarrow x+y+3=0$.