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

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Step 1: Let the ratio be $k : 1$ and point on $y$-axis be $P(0, y)$. Using section formula: $0 = \frac{-k + 5}{k + 1}$
Step 2: $\Rightarrow -k + 5 = 0 \Rightarrow k = 5$. Hence, ratio is $5 : 1$.
Step 3: $y = \frac{-4(5) + (-6)(1)}{5 + 1} = \frac{-20 - 6}{6} = \frac{-26}{6} = -\frac{13}{3}$. Point of intersection is $P\left(0, -\frac{13}{3}\right)$.

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