To write the equation in slope-intercept form \( y = mx + b \), we first need to determine the slope \( m \) using the points from the table. We'll use the points (0, 5) and (2, 1) for our calculations.
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Calculate the slope \( m \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 5}{2 - 0} = \frac{-4}{2} = -2 \]
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Now that we have the slope, we can use one of the points to find the y-intercept \( b \). We'll use the point (0, 5): \[ y = mx + b \implies 5 = -2(0) + b \implies b = 5 \]
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Now we can write the equation in slope-intercept form: \[ y = -2x + 5 \]
Thus, the equation of the line represented by the table is: \[ y = -2x + 5 \] So, in the format requested, the equation is: \[ y = -2x + 5 \]