To find the equation of the linear function that models the relationship shown in the table, we can use the two data points provided: (4, 38) and (6, 58).
-
Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]
-
Use the point-slope form of the linear equation: We use one of the points (let's use (4, 38)) and the slope we just calculated. \[ y - y_1 = m(x - x_1) \] Substituting in the values: \[ y - 38 = 10(x - 4) \]
-
Simplify: \[ y - 38 = 10x - 40 \] \[ y = 10x - 40 + 38 \] \[ y = 10x - 2 \]
The equation of the linear function that models the relationship shown in the table is: \[ \boxed{y = 10x - 2} \]