**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)