To find the equation that represents the nonproportional linear relationship based on the data provided (which seems to be \(x\) and \(y\) values), we would typically look for a pattern to determine the slope and the y-intercept. However, you've only provided the \(x\) values without corresponding \(y\) values or a specific table.
Assuming that you might be looking for a specific linear equation based on the information presented in the responses, let's analyze the options given:
- \(y = -2x + 1\)
- \(y = \frac{1}{2}x + 1\)
- \(y = x + 2\)
- \(y = x + 1\)
Assuming a linear relationship is present, we would need specific points to calculate the slope and intercept.
Let’s assume common values to clarify further (for example, plugging in \(x = -2, 0, 1, 2, 3\)) to calculate y-values based on the equations:
-
For \(y = -2x + 1\):
- \(x = -2\): \(y = 5\)
- \(x = 0\): \(y = 1\)
- \(x = 1\): \(y = -1\)
- \(x = 2\): \(y = -3\)
- \(x = 3\): \(y = -5\)
-
For \(y = \frac{1}{2}x + 1\):
- \(x = -2\): \(y = 0\)
- \(x = 0\): \(y = 1\)
- \(x = 1\): \(y = 1.5\)
- \(x = 2\): \(y = 2\)
- \(x = 3\): \(y = 2.5\)
-
For \(y = x + 2\):
- \(x = -2\): \(y = 0\)
- \(x = 0\): \(y = 2\)
- \(x = 1\): \(y = 3\)
- \(x = 2\): \(y = 4\)
- \(x = 3\): \(y = 5\)
-
For \(y = x + 1\):
- \(x = -2\): \(y = -1\)
- \(x = 0\): \(y = 1\)
- \(x = 1\): \(y = 2\)
- \(x = 2\): \(y = 3\)
- \(x = 3\): \(y = 4\)
Without knowing the actual \(y\) values that correspond to each \(x\), we can't definitively determine which equation represents your data. Please provide the complete data set or clarify the relationships, and I can assist you further. Assuming you have context, I suggest checking against the point pair scenarios and slopes derived from these options.
If you have a specific point from the relationship in mind, you could substitute that point into each equation listed until you find the correct one based on the given responses.