Question:
A line cutting off intercept – 3 from the y-axis and the tangent at angle to the x-axis is 3/5, its equation is
A. 5y – 3x + 15 = 0
B. 3y – 5x + 15 = 0
C. 5y – 3x – 15 = 0
D. None of these
Solution:
A. 5y – 3x + 15 = 0
Explanation:
Given that $\tan \theta=\frac{3}{5}$
We know that,
Slope of a line, $m=\tan \theta$
$\Rightarrow$ Slope of line, $\mathrm{m}=\frac{3}{5}$
Since, the lines cut off intercepts $-3$ on $y$-axis then the line is passing through the point $(0,-3)$.
the point $(0,-3)$.
So, the equation of line is
$y-y_{1}=m\left(x-x_{1}\right)$
$\Rightarrow y-(-3)=\frac{3}{5}(x-0)$
$\Rightarrow y+3=\frac{3}{5} x$
$\Rightarrow 5 y+15=3 x$
$\Rightarrow 5 y-3 x+15=0$
Hence, the correct option is (a)