To find the linear equation in the form \( y = mx + b \), we need to determine the slope (\( m \)) and y-intercept (\( b \)) using the given points (11, 58) and (20, 103).
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Calculate the slope (m): The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, let \((x_1, y_1) = (11, 58)\) and \((x_2, y_2) = (20, 103)\): \[ m = \frac{103 - 58}{20 - 11} = \frac{45}{9} = 5 \]
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Use the slope to find the y-intercept (b): Now that we have the slope \( m = 5 \), we can use one of the points to solve for \( b \). We'll use the point (11, 58): \[ y = mx + b \] \[ 58 = 5(11) + b \] \[ 58 = 55 + b \] \[ b = 58 - 55 \] \[ b = 3 \]
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Write the equation: Substituting \( m \) and \( b \) back into the equation gives: \[ y = 5x + 3 \]
Thus, the equation of the linear function that models the relationship shown in the table is: \[ y = 5x + 3 \]
So the final answer is: y = 5x + 3