The scenario you've described represents a linear relationship between the number of tickets sold (x) and the money earned (y) because there is a constant ratio of money earned per ticket sold, which is proportional.
To determine the constant earnings per ticket, you can calculate the earnings per ticket by dividing the total money earned by the number of tickets sold for each entry. For example:
- For 4 tickets: \( \frac{48}{4} = 12 \)
- For 9 tickets: \( \frac{108}{9} = 12 \)
- For 8 tickets: \( \frac{96}{8} = 12 \)
- For 5 tickets: \( \frac{60}{5} = 12 \)
- For 7 tickets: \( \frac{84}{7} = 12 \)
This shows that every ticket sold earns $12.
The relationship is linear because:
- There is a constant rate of change, which is the earnings of $12 per ticket.
- When 0 tickets are sold, it means $0 is earned, establishing that the relationship passes through the origin (0,0).
So, you can complete the sentence as follows:
Every ticket sold is $12 earned. This is called a linear relationship because there is a constant rate of change, and 0 tickets sold means $0 earned.