In what ratio does the point $P(-4, y)$ divide the line segment joining the points $A(-6, 10)$ and $B(3, -8)$ if it lies on $AB$. Hence find the value of $y$.

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Step 1: Let $AP : PB = k : 1$. $-4 = \frac{3k - 6}{k + 1}$
Step 2: $\Rightarrow k = \frac{2}{7}$. $	herefore AP : PB = 2 : 7$
Step 3: Hence $y = \frac{-8 	imes \frac{2}{7} + 10}{\frac{2}{7} + 1} = \frac{\frac{-16}{7} + 10}{\frac{9}{7}} = \frac{\frac{54}{7}}{\frac{9}{7}} = 6$

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