To find the equation of the linear function that models the relationship between x and y values, we can use the two points given in the table: (6, 16) and (15, 43).
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Find the slope (m): The slope \( m \) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \( (x_1, y_1) = (6, 16) \) and \( (x_2, y_2) = (15, 43) \).
Substituting the values: \[ m = \frac{43 - 16}{15 - 6} = \frac{27}{9} = 3 \]
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Use the slope-intercept form (y = mx + b): Now that we have \( m = 3 \), we can use one of the points to solve for \( b \). Let's use the point (6, 16): \[ y = mx + b \] Substituting \( x = 6 \), \( y = 16 \), and \( m = 3 \): \[ 16 = 3(6) + b \] \[ 16 = 18 + b \] \[ b = 16 - 18 = -2 \]
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Write the final equation: Now we can write the equation of the linear function: \[ y = 3x - 2 \]
So, the equation of the linear function that models the relationship shown in the table is: \[ y = 3x - 2 \]