A super bouncy ball will rebound half of the distance from which it is dropped on each bounce. If it is dropped from a height of 72 inches, how many rebounds will it make? Is this a linear relationship?
The y values in the table are decreasing by different heights on each row, and the x values are increasing by one rebound. Since the changes in the y values are not constant, this function is not linear.
Source: Old Mower, Cavalier92, Flickr
Pedro mows lawns on Saturday to earn extra money. He charges $40 for each lawn he mows. Every Saturday, Pedro must buy gasoline for his lawn mower and plastic bags for the cut grass. His expenses are $32 each Saturday.
Create a table to see if this problem situation has a constant rate of change. Click on the blanks to check your answers.
| Number of Lawns | Pedro's Profit |
|---|---|
0 |
-32 |
1 |
8 |
2 |
|
3 |
Before Pedro mows any lawns, he pays $32. Since this is an expense, it is represented as a negative number.
If Pedro mows one yard, his profit will be $8.
If Pedro mows two yards, his profit will be Interactive button. Assistance may be required. ____ $48.
If Pedro mows three yards, his profit will be Interactive button. Assistance may be required. ____ $88.
What is the change in the x values?
What is the change in the y values?
What is the slope?
Interactive popup. Assistance may be required. Change in x: 1
If y represents Pedro's profit and x represents the number of lawns, what equation represents this relationship?
Is this a linear function, why?
Interactive popup. Assistance may be required. y = 40(x) – 32