To determine the equation of the linear function that models the relationship between \( x \) and \( y \) shown in the table, we need to find the slope \( m \) and the y-intercept \( b \).
We have two points from the table:
\((4, 38)\) and \((6, 58)\).
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Calculate the slope \( m \): The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the values: \[ m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]
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Find the y-intercept \( b \): We will use the slope-intercept form of the equation, which is: \[ y = mx + b \] We can substitute one of the points and our slope into this equation to solve for \( b \). Using the point \((4, 38)\): \[ 38 = 10(4) + b \] \[ 38 = 40 + b \] \[ b = 38 - 40 = -2 \]
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Write the equation: Now that we have \( m = 10 \) and \( b = -2 \), the equation of the line is: \[ y = 10x - 2 \]
Thus, the correct response from the list provided is: y = 10x - 2.
1 answer