To find the equation of the linear function that models the relationship between \( x \) and \( y \) from the table, we can start by identifying the two points provided: \( (4, 38) \) and \( (6, 58) \).
First, we calculate the slope \( m \) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \( (4, 38) \) and \( (6, 58) \):
- \( y_1 = 38 \)
- \( y_2 = 58 \)
- \( x_1 = 4 \)
- \( x_2 = 6 \)
Substituting the values into the slope formula:
\[ m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]
Now we have the slope \( m = 10 \).
Next, we can use the point-slope form of the equation \( y - y_1 = m(x - x_1) \). Using one of our points, let's use \( (4, 38) \):
\[ y - 38 = 10(x - 4) \]
Now, we simplify the equation:
\[ y - 38 = 10x - 40 \] \[ y = 10x - 40 + 38 \] \[ y = 10x - 2 \]
Thus, the equation of the linear function that models the relationship is:
\[ \boxed{y = 10x - 2} \]
Hence, the correct response is \( y = 10x - 2 \).