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| Math Central | Quandaries & Queries |
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Question from Shannon, a student: Find x such that a straight line passing through (2,x) and (x+1, 3) has slope 2x+1/x-1 |
Shannon,
The slope of the line passing through (x1, y1) and (x2, y2) is 
, and hence the slope of the line passing through (2, x) and (x+1, 3) is 
. Thus the problem is to find x if
.
Since the line is to have slope (2x+1)/(x-1) you can not have x = 1 so reduces to
3 - x = 2x + 1.
Solve for x. Verify your answer by showing that for the x value you obtained the slope of the line passing through (2,x) and (x+1, 3) is 2x+1/x-1.
Penny
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