To find the equation of the linear function that models the relationship shown in the table, we can use the points given: (4, 38) and (6, 58).
1. First, we calculate the slope (m) using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (4, 38) and (6, 58):
\[
m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10
\]
2. Now that we have the slope (m = 10), we can use the point-slope form of the equation:
\[
y - y_1 = m(x - x_1)
\]
Let's use the point (4, 38):
\[
y - 38 = 10(x - 4)
\]
Simplifying this, we find:
\[
y - 38 = 10x - 40
\]
\[
y = 10x - 2
\]
Thus, the equation of the linear function that models the relationship shown in the table is:
\[
\boxed{y = 10x - 2}
\]