Question

The equation of the line cutting an intercept of $3$ units on negative $y-$axis and inclined at an angle ${\tan }^{-1}\frac{3}{5}$ to the $x-$axis is

• A. $5y-3x+15=0$
• B. $5y-3x=15$
• C. $3y-5x+15=0$
• D. none of these

Answer 1

The correct option is A $5y-3x+15=0$

The slope-intercept form of a straight line is

$y=mx+c$

Here, $m=\tan \theta =\frac{3}{5}$, $c=-3$

Writing an equation with given values we get

$y=\frac{3}{5}x-3\Rightarrow 5y=3x-15$

$⟹5y-3x+15=0$ is the required equation of a line.