To find the equation representing the given points in a nonproportional linear relationship, we can start by identifying a linear equation in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
The points provided are:
- (-2, -1)
- (0, 1)
- (2, 3)
We can start by determining the slope \(m\) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (0, 1) and (2, 3):
\[ m = \frac{3 - 1}{2 - 0} = \frac{2}{2} = 1 \]
So the slope \(m = 1\).
Next, we can find the y-intercept \(b\) by plugging in the point (0, 1):
\[ y = mx + b \Rightarrow 1 = 1(0) + b \Rightarrow b = 1 \]
Thus, the equation of the line is:
\[ y = 1x + 1 \quad \text{or} \quad y = x + 1 \]
Based on the options provided, the correct response is:
y = x + 1.