To find the linear function that has the same structure as the arithmetic sequence formula \( a_n = 6 + (n - 1) \cdot 8 \), we can rewrite the arithmetic sequence formula in a form that resembles a linear equation.
The formula for the arithmetic sequence can be expanded as follows:
\[ a_n = 6 + 8(n - 1) \] \[ = 6 + 8n - 8 \] \[ = 8n - 2 \]
Now, we have the form \( a_n = 8n - 2 \).
This matches the structure of the linear function \( y = mx + b \), where \( m \) is the coefficient of \( n \) and \( b \) is a constant.
So, the equivalent linear function with the same structure is:
\[ y = 8x - 2 \]
Therefore, the correct response is:
y = 8x - 2.