The table below shows the total cost , in dollars, of hiring a math tutor for hours.
| (hours) | (dollars) |
|---|---|
| 2 | 110 |
| 5 | 200 |
Assuming the relationship between and is linear, what is the cost for each additional hour of tutoring, in dollars?
A linear relationship has the same cost increase for every additional hour. In a two-row table, that hourly rate is the slope: subtract the costs, subtract the matching hours in the same order, then divide in Desmos. Don't divide a total cost by its hours unless you know there is no starting fee.
Hints
- Hint 1
Each row pairs a number of hours with a total cost. The rate of change compares how much the cost rises with how much the hours rise. What changes between the two rows?
- Hint 2
A rate in dollars per hour puts the change in dollars on top and the change in hours underneath. Subtract the second row minus the first row in both places.
Step-by-step
Find the hourly rate from the two rows
Step 1Compare the matching changes
The table pairs hours with $110 and hours with $200. Hours increase by , while cost increases by . Because the relationship is linear, that increase has a constant rate. Divide the change in cost by the change in hours to get dollars per hour:
- Step 2
Calculate and interpret the rate
Type in Desmos. It shows . That's the cost for one additional hour, not the total cost for either row. Each additional hour of tutoring costs $30. Choice B.