Question

Cost for copies is a linear function of the number of copies. If 125 copies cost $29.00, and 175 copies cost $37.00, write a formula for copy cost as a linear function of the number of copies. Then find how much it would cost tomake 700 copies

Answer 1

f(x) = 0.16x + 9

Cost to make 700 copies f(700)= $121

Let y=f(x) be the cost of copies and let x be the number of copies

( 125, 29) and (175, 37)

x₁=125 y₁=29 x₂=175 y₂=37

We first need to find the slope(m) using the formula below:

`\text{slope}(m)=(37-29)/(175-125)`
`=(8)/(50)`
`=0.16`

Next, is to find the intercept (b)

Substitute m=0.16 x=125 and y=29 into y=mx+b and solve for b

29 = 0.16(125) + b

29 = 20 + b

29 - 20 = b

b = 9

The linear function can be formed by substituting m=0.16 and b=9 into the formula y = mx+b

f(x) = 0.16x + 9

To find the cost of 700 copies, substitute x=700 into the above and evaluate.

f(700) = 0.16(700) + 9 = 112 + 9 = $121