Thread: 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.

Originally Posted by Patience

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