To find the equation of the linear function that models the relationship between x and y given in the table, we first need to determine the slope (m) of the line connecting the two points (4, 38) and (6, 58).
The formula for slope \( m \) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points:
- \( (x_1, y_1) = (4, 38) \)
- \( (x_2, y_2) = (6, 58) \)
We calculate:
\[ m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]
Now that we have the slope \( m = 10 \), we can use the point-slope form of the equation, which is:
\[ y - y_1 = m(x - x_1) \]
Substituting \( m = 10 \) and using the point \( (4, 38) \):
\[ y - 38 = 10(x - 4) \]
Now, we simplify this equation:
\[ y - 38 = 10x - 40 \] \[ y = 10x - 40 + 38 \] \[ y = 10x - 2 \]
So, the equation that models the relationship shown in the table is:
\[ y = 10x - 2 \]
Thus, the correct response is:
y = 10x - 2