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A quote: "And while I like solving math problems, what does finding the slope of a line using three different techniques have to do with anything I might do in the future?"

Well, to start, not being killed by underestimating your car's braking distance (which increases as the square of the car's speed). For another, modeling compound interest, the bane of the middle class. For another, the rate of population increase given an annual growth rate, and its meaning for the future of the human race. Just three immediately obvious examples.

If this student doesn't see these obvious applications for math and pre-Calculus, her teachers should be held responsible -- of course, they themselves may not realize all the practical applications of this kind of modeling.