The equation of the straight line passing through the point (-2, 3) and which makes intercepts in the ratio 1 : 3 on the coordinate axes, is

As per the given in the question,

Ratio of intercept $$=\dfrac{1}{3}$$

So, $$x=k$$ and $$y=3k$$

So, the co-ordinates of intersection point on the x and y axis (k,0) and (0,3k)

So, equation of line

$$\Rightarrow (y-0)=\dfrac{3k-0}{0-k}(x-k)$$

$$\Rightarrow y=-3(x-k)$$

Now, this line is passing through the point (-2, 3)

Hence, $$3=-3(-2-k)$$

$$\Rightarrow 3=6+3k$$

$$\Rightarrow k=-1$$

Hence the line equation will be

$$\Rightarrow y=-3x-3$$

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