To determine which equation represents the linear relationship in the table provided, we can first find the slope (m) and y-intercept (b) using the values from the table.
The points from the table are:
- (-4, -3)
- (0, -2)
- (4, -1)
We can use the first two points to calculate the slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - (-3)}{0 - (-4)} = \frac{-2 + 3}{0 + 4} = \frac{1}{4} \]
Now, we can use the slope and one of the points to find the y-intercept (b). Using the point (0, -2):
Using the slope-intercept form of the line \( y = mx + b \):
\[ -2 = \frac{1}{4}(0) + b \implies b = -2 \]
Therefore, the equation in slope-intercept form is:
\[ y = \frac{1}{4}x - 2 \]
This matches the first equation:
y = \frac{1}{4}x - 2.
So, the correct answer is:
y equals one fourth times x minus 2.