Question

Cost for copies is a linear function of the number of copies. If 75 copies cost $23.75, and 100 copies cost $29.00, write a formula for copy cost as a linear function of the number of copies. Then find how it would cost to make 900 copies.

Answer 1

It would cost $261.

Explanation:

If 100 copies costs $29.00, then you can simply multiply $29.00 times 9.

29·9=261

Answer 2

y = cost of making 900 copies = $197.00

Explanation:

Imagine a straight line passing thru the points (75, $23.75) and (100, $29.00). As we move from x = 75 to x = 100 (an increase of 25), y moves from $23.75 to $29.00 (an increase of $5.25.

Thus, the slope of this line would be m = rise / run = $5.25 / 25, or $0.21 / copy.

Using the point-slope formula for the equation of a straight line:

y - k = m (x - h), or, specifically, y - $29.00 = ($0.21 / copy)(x - 100)

The cost to make 900 copies is found by substituting 900 for x in the above equation:

y - $29.00 = ($0.21 / copy)(900 - 100), or

y - $29.00 = ($0.21 / copy)(800), or y - $29.00 + $168

y = cost of making 900 copies = $197.00