Step 1 :Given the equation \(y = -4x + 8\), we need to find the equation that has infinitely many intersection points with it.
Step 2 :Check each option:
Step 3 :(1) \(4x - y - 8 = 0\) has the solution \(x = 2, y = 0\), which is not the same as the given equation.
Step 4 :(2) \(4x - y + 8 = 0\) has the solution \(x = 0, y = 8\), which is not the same as the given equation.
Step 5 :(3) \(y - 4x - 8 = 0\) has the solution \(x = 0, y = 8\), which is not the same as the given equation.
Step 6 :(4) \(y + 4x - 8 = 0\) has the solution \(x = 2 - \frac{y}{4}\), which has infinitely many intersection points with the given equation.
Step 7 :(5) \(y + 4x + 8 = 0\) has no solution.
Step 8 :\(\boxed{\text{Final Answer: (4) } y + 4x - 8 = 0}\)