Question

Write an equation for expense (blue line)

Answer 1

Answer:  y = 0.0005x+1

This is the same as saying y = (1/2000)x + 1

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Explanation:

The blue line goes through (0,1) and (2000,2)

The slope is

m = (y2-y1)/(x2-x1)

m = (2-1)/(2000-0)

m = 1/2000

This says that each time we move up 1, we move to the right 2000 units.

Think of it as slope = rise/run = 1/2000

The slope 1/2000 means that each time you make 2000 soccer balls, it will cost you $1000. Keep in mind that y is in thousands (eg: y = 1 means 1000). This further implies that the marginal cost is ($1000)/2000 = $0.50 = 50 cents. The marginal cost is the cost to make one extra unit.

The fraction 1/2000 converts to the decimal form 0.0005 after using a calculator. So m = 0.0005 is the decimal form of the slope.

The y intercept of the blue line is b = 1 as this is the location where the blue line crosses the vertical y axis. The y intercept represents the fixed costs needed to set up production, for example: buying the machinery needed is a fixed cost.

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Since m = 0.0005 and b = 1, we go from y = mx+b to y = 0.0005x+1

We could say y = (1/2000)x + 1, though I think it's probably easier to use a decimal in this case.