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Question

Find the slope of a line passing through the following points:
(i) (−3, 2) and (1, 4)
(ii) (at12, 2 at1) and (at22, 2 at2)
(iii) (3, −5), and (1, 2)

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Solution

(i) (−3, 2) and (1, 4)

Let m be the slope of the given line.

m=y2-y1x2-x1m=4-21+3=24=12

Hence, the slope of the line passing through the points (−3, 2) and (1, 4) is 12.

(ii) (at12, 2at1) and (at22, 2at2)

Let m be the slope of the given line.

m=y2-y1x2-x1m=2at2-2at1at22-at12=2t2-t1t2-t1t2+t1=2t1+t2

Hence, the slope of the line passing through the points (at12, 2at1) and (at22, 2at2) is 2t1+t2.

(iii) (3, −5), and (1, 2)

Let m be the slope of the given line.

m=y2-y1x2-x1m=2+51-3=-72

Hence, the slope of the line passing through the points (3, −5), and (1, 2) is -72.

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