To determine the correct equation that models the linear relationship from a table of values, we first need to look for the slope (m) and y-intercept (b).
Steps to Find the Equation in Slope-Intercept Form (y = mx + b):
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Identify two points from the table: You need at least two points to calculate the slope. A point is typically represented as (x, y).
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Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
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Find the y-intercept (b): You can use one of the points and the slope in the equation \(y = mx + b\) to solve for b. Rearranging gives \(b = y - mx\).
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Write the equation in slope-intercept form.
Without the actual table, I can't compute the values directly. However, I can demonstrate how to do it. You can follow these steps with the values from your table.
Example Calculation:
Suppose you found two points: (1, 1) and (3, 5).
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Calculate the slope: \[ m = \frac{5 - 1}{3 - 1} = \frac{4}{2} = 2 \]
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Choose one of the points, say (1, 1), to find b: \[ 1 = 2(1) + b \rightarrow b = 1 - 2 = -1 \]
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Write the equation: \[ y = 2x - 1 \]
Using this procedure, you will arrive at the linear equation. Based on the response options provided, after calculating the slope and intercept with your values, you will select the equation that matches your results.
If you can provide the specific values from the table, I can assist you further in determining the exact equation.
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