To determine if the table represents a linear function, we need to check if the change in \(y\) divided by the change in \(x\) (the slope) is constant.
Given the points:
- \( (5, -9) \)
- \( (7, -6) \)
We can calculate the slope \(m\) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \( (x_1, y_1) = (5, -9) \) and \( (x_2, y_2) = (7, -6) \).
Calculating the differences:
\[ y_2 - y_1 = -6 - (-9) = -6 + 9 = 3 \] \[ x_2 - x_1 = 7 - 5 = 2 \]
Now, substituting these values into the slope formula:
\[ m = \frac{3}{2} \]
Since we have a defined slope between the two points, the table does represent a linear function.
Conclusion: Yes, this table represents a linear function, and the slope is \(\frac{3}{2}\).
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