To determine the linear equation that represents the given nonproportional linear relationship, we can analyze the provided points.
The points from the table are:
- (-5, 0)
- (0, 5)
- (2, 7)
Let's use two of the points to calculate the slope (m) of the line. We can take the points (0, 5) and (2, 7).
The formula for the slope (m) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using (0, 5) as (x_1, y_1) and (2, 7) as (x_2, y_2): \[ m = \frac{7 - 5}{2 - 0} = \frac{2}{2} = 1 \]
With the slope (m) of 1, we can use the point-slope form of the equation:
\[ y - y_1 = m(x - x_1) \]
Using the point (0, 5): \[ y - 5 = 1(x - 0) \] \[ y - 5 = x \] \[ y = x + 5 \]
Now, let's check the equation against the remaining points to confirm consistency with the nonproportional relationship:
- For x = -5: \( y = -5 + 5 = 0 \) (matches the point (-5, 0))
- For x = 2: \( y = 2 + 5 = 7 \) (matches the point (2, 7))
Thus, the equation \( y = x + 5 \) accurately represents the nonproportional linear relationship.
The correct response is: y = x + 5