To find the equation of the linear function that models the relationship shown in the table, we can first identify the two points given: (4, 38) and (6, 58).
Next, we need to calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Where:
- \( (x_1, y_1) = (4, 38) \)
- \( (x_2, y_2) = (6, 58) \)
Plugging in the values: \[ m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]
Now, we have the slope \( m = 10 \). Next, we use the slope-intercept form of a linear equation, \( y = mx + b \), to find the y-intercept \( b \).
We can use one of the points to find \( b \). Let's use the point (4, 38): \[ 38 = 10(4) + b \] \[ 38 = 40 + b \] \[ b = 38 - 40 = -2 \]
Now we can write the equation of the line: \[ y = 10x - 2 \]
Thus, the equation of the linear function that models the relationship shown in the table is: \[ \boxed{y = 10x - 2} \]