Answer: c(x) = y = $0.132*x + $27.16
Step-by-step explanation:
The chargers are a fixed price plus a charge for every copy, then we have a linear relationship.
A linear relationship can be written as:
c(x) = y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case, c(x) = y represents the cost in dollars, x is the number of copies bought, and b is the fixed cost.
We know two points in this line:
(80, $37) and (209, $54)
Whit those two points we can find the slope:
a = ($54 - $37)/(209 - 80) = $17/129 = $0.132 per copy.
Then our equation is:
c(x) = y = $0.132*x + b
To find the value of b, we know that 80 copies cost $37, we can replace those values in the equation:
$37 = $0.132*80 + b
$37 = $9.84 + b
($37 - $9.84) = $27.16 = b.
Then the equation is:
c(x) = y = $0.132*x + $27.16
