In a certain city the cost for a taxi ride for 20 miles is $13. For 30 miles the cost is $18. Assuming the number of miles is x find the lin

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In a certain city the cost for a taxi ride for 20 miles is $13. For 30 miles the cost is $18. Assuming the number of miles is x find the linear equation for the cost.

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    2021-11-23T21:08:35+00:00

    We need to write the linear equation that is satisfied by (20,13) and (30,18).
                                 $18 – $13         $5
    The slope is m = ————— = ——– = $0.50/mile
                                  30 – 20            10

    We need to find the y-intercept of this function.  To do that, start with the slope-intercept form   y = mx + b

    and subst. the y and x values from one of the two given points.  Suppose we choose (20,$13):

    $13 = ($0.50/mile)(20 miles) + b

    Then $13 = $10 + b, and b = $3.

    There’s an up-front charge of $3 just to step into the taxi.

    The equation in question is y = ($0.50/mile)x + $3.00           (answer)

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