To find the equation of the line in the form \( y = mx + b \), we first need to determine the slope \( m \) and the y-intercept \( b \).
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Calculate the slope \( m \): The slope \( m \) is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] We can use any two points from the table. Let's use the points (0, 7) and (3, 1).
\[ m = \frac{1 - 7}{3 - 0} = \frac{-6}{3} = -2 \]
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Find the y-intercept \( b \): The y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the table, we can see that when \( x = 0, y = 7 \). Thus, \( b = 7 \).
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Write the equation: Now we can write the equation in slope-intercept form \( y = mx + b \): \[ y = -2x + 7 \]
So, the equation of the line in slope-intercept form is: \[ y = -2x + 7 \]