To find the equation of the nonproportional linear relationship given the points from the table, we can use the coordinates provided:
- When \( x = -2 \), \( y = -1 \)
- When \( x = 0 \), \( y = 1 \)
- When \( x = 2 \), \( y = 3 \)
First, we can find the slope (m) of the line using two points. Let's use the points \( (0, 1) \) and \( (2, 3) \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 1}{2 - 0} = \frac{2}{2} = 1 \]
Now that we have the slope \( m = 1 \), we can use the point-slope form of the equation \( y - y_1 = m(x - x_1) \). Let's use the point \( (0, 1) \):
\[ y - 1 = 1(x - 0) \] \[ y - 1 = x \] \[ y = x + 1 \]
Therefore, the equation that represents the nonproportional linear relationship is:
\[ \boxed{y = x + 1} \]