To determine the equation that represents the relationship given the points in the table, we first need to identify the coordinates that are represented by the data. Based on your input, the points appear to be:
- (0, 1)
- (2, 3)
Now, let's calculate the slope (m) of the linear relationship using the two points:
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Use the formula for the slope: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in our points:
- \((x_1, y_1) = (0, 1)\)
- \((x_2, y_2) = (2, 3)\)
\[ m = \frac{3 - 1}{2 - 0} = \frac{2}{2} = 1 \]
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Now that we know the slope \(m = 1\), we can use the point-slope form of the equation to find the linear equation: \[ y - y_1 = m(x - x_1) \] Using the point (0, 1): \[ y - 1 = 1(x - 0) \] Simplifying this: \[ y - 1 = x \] \[ y = x + 1 \]
Thus, the equation that represents the nonproportional linear relationship based on the points provided is: \[ y = x + 1 \]
This matches with one of your provided choices.