To find the equation of the linear function that models the relationship shown in the table, we need to determine the slope \( m \) and the y-intercept \( b \) of the line.
We have two points from the table:
- \( (4, 38) \)
- \( (6, 58) \)
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting in our points: \[ m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]
Now we have the slope \( m = 10 \).
Next, we can use one of the points and the slope to find the y-intercept \( b \) using the equation of a line \( y = mx + b \). Let's use the point \( (4, 38) \): \[ 38 = 10(4) + b \] \[ 38 = 40 + b \] \[ b = 38 - 40 = -2 \]
So, the equation of the linear function is: \[ y = 10x - 2 \]
Thus, the correct response is: y = 10x - 2