To determine if the points represent a linear function, we can check if the change in \( y \) (the vertical change) over the change in \( x \) (the horizontal change) is constant.
You have two points:
- \((-4, 1)\)
- \((0, 2)\)
Now, let's calculate the slope \( m \) using the formula for slope:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in the coordinates of the points:
- \( (x_1, y_1) = (-4, 1) \)
- \( (x_2, y_2) = (0, 2) \)
\[ m = \frac{2 - 1}{0 - (-4)} = \frac{1}{4} \]
Since you have a constant slope, the table does represent a linear function.
Therefore, yes, it is a linear function, and the slope is \( \frac{1}{4} \).
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