To find the rate of change of the values in the table, we can calculate the differences in the \( y \) values and divide them by the differences in the \( x \) values.
The rate of change can be calculated using the formula:
\[ \text{Rate of Change} = \frac{\Delta y}{\Delta x} \]
Let's calculate the change in \( y \) for each change in \( x \):
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From \( x = 1 \) to \( x = 2 \): \( \Delta y = 19 - 12 = 7 \); \( \Delta x = 2 - 1 = 1 \); Rate of Change = \( \frac{7}{1} = 7 \)
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From \( x = 2 \) to \( x = 3 \): \( \Delta y = 26 - 19 = 7 \); \( \Delta x = 3 - 2 = 1 \); Rate of Change = \( \frac{7}{1} = 7 \)
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From \( x = 3 \) to \( x = 4 \): \( \Delta y = 33 - 26 = 7 \); \( \Delta x = 4 - 3 = 1 \); Rate of Change = \( \frac{7}{1} = 7 \)
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From \( x = 4 \) to \( x = 5 \): \( \Delta y = 40 - 33 = 7 \); \( \Delta x = 5 - 4 = 1 \); Rate of Change = \( \frac{7}{1} = 7 \)
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From \( x = 5 \) to \( x = 6 \): \( \Delta y = 47 - 40 = 7 \); \( \Delta x = 6 - 5 = 1 \); Rate of Change = \( \frac{7}{1} = 7 \)
Thus, the rate of change between each pair of \( x \) values is consistently \( 7 \).
Therefore, the overall rate of change for the data in the table is 7.