Question

Find the equation to the straight line cutting off an intercept $-3$ from the axis of $y$ and inclined at an angle ${\tan }^{-1}\frac{3}{5}$ to the axis of $x$.

Answer 1

Here,

$\tan \theta =\frac{3}{5}=\frac{3}{x}$

$\Rightarrow x=5$

And, $\frac{y}{-3}+\frac{x}{5}=1$

$\Rightarrow 3x-5y=15$

Therefore, required equation is

$5y-3x+15=0$