A line passes through $(x_{1}, y_{1})$ and (h, k). If slope of the line is m, show that $k - y_{1} = m (h - x_{1})$ .

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Solution

Let $A (x_{1}, y_{1})$ and B(h, k) be two points.

$∴$ Slope of $A B = \frac{k - y_{1}}{h - x_{1}}$

Slope of AB = m (given)

$∴ m = \frac{k - y_{1}}{h - x_{1}} \Rightarrow k - y_{1} = m (h - x_{1})$

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