To find the equation of the linear function that models the relationship shown in the table, we need to determine the slope (\(m\)) and the y-intercept (\(b\)) of the line that connects the points (4, 38) and (6, 58).
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Calculate the slope (\(m\)): The formula for slope is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (4, 38) and (6, 58): \[ m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]
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Use the point-slope form to find the y-intercept (\(b\)): The equation of a line is usually written as: \[ y = mx + b \] We can use one of the points to find \(b\). Let's use the point (4, 38): \[ 38 = 10(4) + b \] \[ 38 = 40 + b \] \[ b = 38 - 40 = -2 \]
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Write the equation: Now substitute \(m = 10\) and \(b = -2\) into the equation: \[ y = 10x - 2 \]
So, the equation of the linear function that models the relationship shown in the table is: \[ \boxed{y = 10x - 2} \]