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Line PQ is parallel to line RS where points P,Q,R and S have co-ordinates (2, 4), (3, 6), (3, 1) and (5, k) respectively. Find value of k. 

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Slope of the line = y2 - y1 / x2 - x1

P(2, 4), Q(3, 6) 

slope of the line PQ = 6 - 4 / 3 - 2 = 2 / 1 = 2

R(3, 1), S (5, k)

slope of the line RS = k -1 / 5 - 3 = k −1 / 2

But line PQ || line RS 

∴ slope of line PQ = slope of line RS

∴ 2 = k −1 / 2 

∴ 4 = k - 1 

∴ 4 + 1 = k 

∴ k = 5

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