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The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May her driving cost was $380 for 480 mi and in June her cost was $450 for 830 mi. Assume that there is a linear relationship between the monthly cost C of driving a car and the distance x driven. Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a suitable model.

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  1. Today, 01:22
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    Answer: the model is

    C (x) = 0.2x + 284

    Step-by-step explanation:

    let x represent the distance driven in a month.

    Let y represent the monthly cost for driving x miles.

    If we plot y on the vertical axis and x on the horizontal axis, a straight line would be formed. The slope of the straight line would be

    Slope, m = (450 - 380) / (830 - 480)

    m = 70/350 = 0.2

    The equation of the straight line can be represented in the slope-intercept form, y = mx + c

    Where

    c = intercept

    m = slope

    To determine the intercept, we would substitute x = 480, y = 380 and m = 0.2 into y = mx + c. It becomes

    380 = 0.2 * 480 + c

    380 = 96 + c

    c = 380 - 96

    c = 284

    Therefore, the linear model is

    y = 0.2x + 284

    C (x) = 0.2x + 284
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