Find the ratio in which the y-axis divides the line segment joining the points $\displaystyle (5, -6)$ and $\displaystyle (-1, -4)$. Also find the point of intersection.

Let the ratio be k:$\displaystyle 1$ and point on y- axis be P($\displaystyle 0$, y) \[\begin{aligned} 0 & =\frac{-\mathrm{k}+5}{\mathrm{k}+1} \\ \mathrm{k} & =5 \end{aligned} \] Hence, ratio is $\displaystyle 5$:$\displaystyle 1$ \[y=\frac{-4(5)-6}{5+1}=\frac{-26}{6}=\frac{-13}{3} \] Coordinates of point of intersection are \(\displaystyle \mathrm{P}\left(0,-\frac{13}{3}\right)\)