Given the values in the table you've provided, we can analyze the relationship between the number of tickets sold (x) and the money earned (y) to fill in the blanks.
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Every ticket sold is \(12\) dollars earned. This can be determined by dividing the total earnings by the number of tickets sold for any given point:
- For example, for \(x = 4\) tickets sold, \(y = 48\) dollars earned. Thus, \(48 / 4 = 12\).
- Similarly, for other points, you will find \(y / x = 12\).
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This is called a linear relationship. The relationship is linear when you can express it in the form \(y = mx\), where \(m\) is the slope, indicating a constant change.
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The relationship is proportional. In this case, the amount earned is directly proportional to the number of tickets sold because as you sell more tickets, you earn proportionally more money.
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because there is a constant rate of change. The fact that each ticket sold earns a consistent amount (12 dollars) means there’s a constant ratio between the two variables.
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and 0 tickets sold means $0 earned. This confirms the proportional relationship, as selling zero tickets results in zero earnings, which confirms that the relationship goes through the origin (0,0).
Putting it all together, the completed sentences would read:
- Every ticket sold is 12 dollars earned. This is called a linear relationship. The relationship is proportional because there is a constant rate of change and 0 tickets sold means $0 earned.