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Math Help - write linear equation and in slope-intercept form

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    write linear equation and in slope-intercept form

    In planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x.
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    Quote Originally Posted by Patience View Post
    In planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x.
    we will plot the cost on the y-axis and the number of items produced on the x-axis. thus the linear equation we seek is of the form:

    C = mx + b .......where m is the slope of the line and b is the y-intercept.

    so we have the points (100, 10000) and (300, 22000)

    thus, the slope is given by (y2 - y1)/(x2 - x1)

    => m = (22000 - 10000)/(300 - 100) = 12000/200 = 60

    so now for the equation of the line, we will use the point-slope form
    => C - C1 = m(x - x1)
    => C - 10000 = 60(x - 100)
    => C = 60x - 6000 + 10000
    => C = 60x + 4000
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