The ratio in which the straight line 3 x + 4 y = 6 divides the join of the points ( 2 , - 1 ) and ( 1 , 1 ) is

Let, the line $3x+4y=6$ divides the line segment joining the points $P\left(2, -1\right)$ and $Q\left(1, 1\right)$ in ratio $k : 1$.

Hence, the point of intersection is $\left(\frac{2+k}{k+1}, \frac{-1+k}{k+1}\right)$, which lies on the line $3x+4y=6$ .

So, $3\left(\frac{2+k}{k+1}\right)+4\left(\frac{-1+k}{k+1}\right)=6 \Rightarrow 6+3k-4+4k=6k+6 \Rightarrow k=4$

Hence, the ratio is $4 : 1$.