ShmoopTube

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Slope, a la Shmoop. Marvin's Lemonade Stand is off to a slow start.

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It could be because Marvin sells his customers glasses full of lemons and tells them to make

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their own lemonade. Mmm. Motivational and delicious.

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Marvin sells his glass o' lemons at two dollars per glass.

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He starts the day with $10 and sells 4 glasses per hour.

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If we plotted the money Marvin earns for every hour that his lemonade stand is open...

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...what would be the slope of the line? First, we want to know which two values our

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line represents. We're trying to relate the time that the stand

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is open, in hours... ...to the money Marvin earns, in dollars.

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So... we want to assign our variables properly. The independent variable is x, and the dependent

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variable is y. Since the money Marvin earns depends on the

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number of hours that pass... ...we know that time will be on our x axis

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Time is gonna pass no matter what ... making it an independent value or variable.

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Which makes money our y axis because it is DEPENDENT on the time

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Slope is "rise" over "run," or y over x... ...so we know that our units should be in

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dollars per hour. If Marvin sells 4 glasses at $2 apiece...

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...he'll earn $8 per hour. So the slop of our line is... 8.

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The equation of the line would be y equals 8x plus 10...

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...because Marvin starts out with $10 originally... ...and every hour that passes x, he earns

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eight more dollars... ...which is reflected in his total dollar

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amount... y. However, one of his loyal customers choked

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on a lemon... ...and the slope cost of hiring a lawyer is

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a whole different matter.

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