|연립방정식의 해의 개수와 그래프의 위치관계 | 정답률 $63 \%$
78 다음 일차함수의 그래프 중 일차함수 $y=-4 x+8$ 의 그래프와 교점이 무수히 많이 생기는 경우는?
(1) $4 x-8-y=0$
(2) $4 x-y+8=0$
(3) $y-4 x-8=0$
(4) $y+4 x-8=0$
(5) $y+4 x+8=0$

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 ：\(\boxed{\text{Final Answer: (4) } y + 4x - 8 = 0}\)