To determine the slope of the line defined by the points in the table, you can use the formula for slope (m), which is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
You can use any two points from the table to calculate the slope. Let's use the points \((-2, 1)\) and \( (2, 2) \).
Here, \( (x_1, y_1) = (-2, 1) \) and \( (x_2, y_2) = (2, 2) \).
Now substitute the values into the slope formula:
\[ m = \frac{2 - 1}{2 - (-2)} = \frac{1}{2 + 2} = \frac{1}{4} \]
So the slope is \(\frac{1}{4}\).
Let's check another pair of points, \( (2, 2) \) and \( (10, 4) \):
Here, \( (x_1, y_1) = (2, 2) \) and \( (x_2, y_2) = (10, 4) \).
Now substitute these values into the slope formula:
\[ m = \frac{4 - 2}{10 - 2} = \frac{2}{8} = \frac{1}{4} \]
The slope remains consistent.
The slope of the line is \(\frac{1}{4}\).
So, the correct response from your options is:
\(\frac{1}{4}\).