To find the equation that represents the nonproportional linear relationship given the points \( (-12, -1) \), \( (0, 1) \), and \( (2, 3) \), we first need to determine the slope \( m \) of the line.
- Calculate the slope \( m \) using two of the points. Let's use \( (0, 1) \) and \( (2, 3) \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 1}{2 - 0} = \frac{2}{2} = 1 \]
- Now we have the slope \( m = 1 \). We can use the point-slope form of the equation of a line to find the y-intercept \( b \):
Using the point \( (0, 1) \):
\[ y = mx + b \]
Substitute \( m \) and the coordinates of the point:
\[ 1 = 1(0) + b \implies b = 1 \]
Therefore, the equation of the line is:
\[ y = 1x + 1 \quad \text{or simply} \quad y = x + 1 \]
From the options given, the correct equation that represents this nonproportional linear relationship is:
y = x + 1.