A linear model for a printing charge has a constant price per page and may also have a fixed charge. Two bills at different page counts give you the price per page: divide the change in cost by the change in pages. Then use one bill to find the fixed charge. A bill for several pages is not the charge for zero pages.
Hints
- Hint 1
The slope is the change in cost for each additional page. Compare the change between the two bills with the change between their page counts. Which change belongs on top of the fraction?
- Hint 2
In , is the price per page and is the intercept, the charge at zero pages. Substitute a page count and its matching bill to find .
Step-by-step
Find the rate, then the fixed charge
Step 1Pair each page count with its bill
Each bill gives a point , with pages first and dollars second: and . Keep each page count paired with its cost when you compare the bills.
- Step 2
Find the price per page
The slope is the change in dollars divided by the change in pages. Type in Desmos; it shows . So the charge rises $0.10 per page. Divide by the full change of pages, not by either page count.
- Step 3
Use a bill to write the fixed-charge equation
Write the linear model as , where is the charge when . The 300-page bill gives . The $54 total is not the fixed charge because it includes 300 pages.
- Step 4
Solve for the fixed charge
Type in Desmos. The asks it to solve the equation for ; under PARAMETERS, it shows . So the intercept, or charge for zero pages, is $24.
- Step 5
Write the total-charge equation
Combine the slope with the $24 fixed charge: . This gives the total monthly charge, in dollars, for pages. Choice A.