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 data points:
- \( (-1, 1) \)
- \( (1, -3) \)
- \( (3, -7) \)
- \( (5, -11) \)
Let's calculate the slope between each pair of consecutive points:
-
From \((-1, 1)\) to \( (1, -3)\): \[ \text{slope} = \frac{-3 - 1}{1 - (-1)} = \frac{-4}{2} = -2 \]
-
From \( (1, -3)\) to \( (3, -7)\): \[ \text{slope} = \frac{-7 - (-3)}{3 - 1} = \frac{-4}{2} = -2 \]
-
From \( (3, -7)\) to \( (5, -11)\): \[ \text{slope} = \frac{-11 - (-7)}{5 - 3} = \frac{-4}{2} = -2 \]
Since the slope is consistently \(-2\) for each pair of points, the table does represent a linear function.
Conclusion: Yes, the table represents a linear function with a slope of \(-2\).