If x is the number of copies made and y is the amount charged for the​ copies, what is the formula for the amount​ charged?

Question

Cost for copies is a linear function of the number of copies. If 75 copies cost $17.25​, and 100 copies cost $22.00​, write a formula for copy cost as a linear function of the number of copies. Then find how much it would cost to make 800 copies.

The formula is y=

Answer 1

This being a linear function it will be completely determined by two points.

These points are given as (75 copies, $17.25) and (100 copies, $22).

We can assume a slope-intercept form of Y = m X + b.

The slope m can be found using the slope formula m = (y₂ - y₁)/(x₂-x₁).

So here m = (22 - 17.25)/(100 - 75). This simplifies to m = 4.75 / 25 or m = 0.19

So now we have Y = 0.19 X + b, and we can use either point to plug in and solve for b.

Choosing (100 copies, $22) we see that 22 = 0.19 * 100 + b or 22 = 19 + b so b = 22 - 19 = 3.

So we get the cost Y as a function of the number of copies X is Y = 0.19 X + 3 and that X = 800 copies will cost Y = 0.19 * 800 + 3 = $155.

Hope this helps! Let me know if I can explain any steps in more detail. Thank you!

Answer 2

Look up how to write the equation of a line when you are given 2 points.

For your example let y = cost, x = number of copies.

Your two points are (75, 17.25) and (100, 22). Give it a try and show your attempt here. We can let you know how you did. Good luck!