To determine the linear equation that represents the non-proportional linear relationship for the given points, we can use the points in the table to find the slope (m) and the y-intercept (b) of the line in the slope-intercept form, which is \( y = mx + b \).
Let's take two points from the table to find the slope:
- Point (-5, 0)
- Point (0, 5)
The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the points (-5, 0) and (0, 5):
\[ m = \frac{5 - 0}{0 - (-5)} = \frac{5}{5} = 1 \]
Now that we have the slope \( m = 1 \), we can use the y-intercept (b) found from the point (0, 5), where when \( x = 0 \), \( y = 5 \). Thus, the y-intercept \( b = 5 \).
Now we can write the equation:
\[ y = mx + b \implies y = 1x + 5 \implies y = x + 5 \]
Therefore, the equation that represents the non-proportional linear relationship is:
y = x + 5
This matches the response option.