To determine if the given data represents a linear function, we can check if the slope between the two points is constant.
The given points are:
- \( (4, 0) \)
- \( (-1, 2) \)
The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using our points:
- \( (x_1, y_1) = (4, 0) \)
- \( (x_2, y_2) = (-1, 2) \)
Substituting these values into the slope formula, we get:
\[ m = \frac{2 - 0}{-1 - 4} = \frac{2}{-5} = -\frac{2}{5} \]
Since we have a consistent slope, the table represents a linear function, and the slope is \( -\frac{2}{5} \).