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2018 AMC 12B Problem 3

Problem 3 of 25EasierAlgebraGeometry

A line with slope 22 intersects a line with slope 66 at the point (40,30).(40, 30). What is the distance between the xx-intercepts of these two lines?

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Solution

The line of slope 22 is y−30=2(x−40);y-30=2(x-40); setting y=0y=0 gives x=25.x=25. The line of slope 66 is y−30=6(x−40);y-30=6(x-40); setting y=0y=0 gives x=35.x=35. The distance between the intercepts is ∣35−25∣=10.|35-25|=10. Thus, the correct answer is B.

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Concepts: linear equation · slope · coordinate geometry

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.