To find the linear equation that represents the nonproportional linear relationship between the coordinates given in the table, we can start by identifying the points and their corresponding values. The points given in the table are (0, 0), (2, 7), and (5, 1).
We will use these points to determine the slope (m) of the linear equation in the slope-intercept form, \( y = mx + b \).
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Calculate the slope (m) using the points (2, 7) and (0, 0):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 0}{2 - 0} = \frac{7}{2} \]
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Find y-intercept (b) using one of the points. Using the point (0, 0):
Since \( y = mx + b \) at \( (0, 0) \):
\[ 0 = \frac{7}{2}(0) + b \implies b = 0 \]
Thus, our linear equation based on the slope and the y-intercept is:
\[ y = \frac{7}{2}x \]
However, none of the provided equations match this form directly.
Therefore, we'll check each candidate:
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\( y = x + 5 \) - Substitute (2,7): \[ 7 \neq 2 + 5 \]
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\( y = -5x + 5 \) - Substitute (2, 7): \[ 7 \neq -5(2) + 5 \]
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\( y = -x + 5 \) - Substitute (2, 7): \[ 7 \neq -2 + 5 \]
Out of the provided equations, it seems we are looking for the best fitting context. The relationship does not appear to be straightforward compared with the table and selections provided.
Thus, based on checking through alternatives, the most appropriate and closest fit may not exactly represent \( y = \frac{7}{2}x \) or \( y = mx + b \) specifically but does indicate strong reliance on command terms of significance in both y-intercept and slope as processed.
The best option that may match based on slope is:
None of the choices provided fully represent a correct response to the points given. They rather misdirect values from initial slope calculations made (respecting table accuracy). If forced to select, choose "y = -x + 5" although no exact fit. Please clarify or validate context, as linear representations do not derive directly from above abnormalities.
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