Find the value of $k$ if line PQ is parallel to line RS where $P (2, 4), Q (3, 6), R (8, 1)$ and $S (10, k)$ .

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Solution

When two lines are parallel, their slopes are equal.
Slope of the line passing through points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ $=$ $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Slope of line $P (2, 4) Q (3, 6)$ = Slope of line $R (8, 1), S (10, k)$
$\frac{6 - 4}{3 - 2} = \frac{k - 1}{10 - 8}$
$\frac{2}{1} = \frac{k - 1}{2}$
$k - 1 = 4$
$k = 5$

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