To find the equation that represents the relationship between \( z \) (the number of events) and \( y \) (the number of medals awarded), we can look at the pattern in the table.
From the description, we know that in every Olympic event, 3 medals are awarded. Therefore, the total number of medals awarded \( y \) is equal to the number of events \( z \) multiplied by 3.
So the equation can be expressed as:
\[ y = 3z \]
To verify this with the values in the table:
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For \( z = 7 \): \[ y = 3 \times 7 = 21 \]
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For \( z = 8 \): \[ y = 3 \times 8 = 24 \]
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For \( z = 9 \): \[ y = 3 \times 9 = 27 \]
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For \( z = 10 \): \[ y = 3 \times 10 = 30 \]
All these calculations confirm that the relationship holds true. Therefore, the equation representing the relationship is:
\[ y = 3z \]