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4 August, 03:06

Henry is driving to Boston. Suppose that the remaining distance to drive in miles is a linear function of his driving time in minutes). When graphed, the function gives a line with a slope of - 0.95. Henry has 55 miles remaining after 44 minutes of driving. How many miles will be remaining after 64 minutes of driving.

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  1. 4 August, 03:36
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    When it says that remaining distance is a linear function of time, this means that the remaining distance depends on time. since we know y depends on x we will say remaining distance is y and time is x. so we have a basic equation of

    y = mx + b

    where slope is m, y is remaining distance, x is time, and b is a constant

    it says the slope of lineis - 0.95. sub that in for m and get

    y = - 0.95x + b

    it says 55 remaining distance after 44 time. so we have a x and y

    55 = - 0.95 (44) + b

    55 = - 41.8 + b

    96.8 = b

    we now have b

    y = - 0.95x + 96.8

    it asks for remaining distance after 64 time. we have an x and must solve for y

    y = - 0.95 (64) + 96.8

    y = 36 miles
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