A linear function adds the same amount to the total for each extra item. With two table rows, find that amount, called the slope, by dividing the change in dollars by the change in items; Desmos can evaluate the fraction. Then add the change for the extra items to a known total. Don't divide one total by its item count unless you know the total at zero is zero.
Hints
- Hint 1
Each input-output pair keeps a bottle count with its total. Neither row tells you the amount collected at zero bottles, so don't treat either total as the starting amount.
- Hint 2
The slope is dollars added per bottle. Compare the two totals, then divide by how many more bottles were sold. What increase does that give for one bottle?
- Hint 3
Use a known total as your anchor. How many more bottles are sold at the requested count than at bottles, and how many dollars does the slope add?
Step-by-step
Find the rate, then extend a table row
Step 1Read the table as paired values
Each input-output pair matches a bottle count with its total: the rows give and . The club collected $38 at bottles, not at zero, so don't use $38 as the starting amount.
- Step 2
Find the increase per bottle
The slope is the change in dollars for one more bottle. Type into Desmos; it shows . Dollars go on top and bottles on the bottom, with the rows subtracted in the same order. So each extra bottle adds $7.
- Step 3
Extend from a known total
Start from the $80 collected at bottles. Type in Desmos to add $7 for each additional bottle. It shows , the total collected for bottles. Start from a known row, then add the rate for the extra bottles. Grid in 115.