Final answer:
The relationship between the two given equations is that they are perpendicular to each other.
Step-by-step explanation:
The two given equations are y = 4x + 3 and y = -(1/4)x - 9. To determine the relationship between these equations, we need to compare their slopes.
The slope of the first equation, y = 4x + 3, is 4. The slope of the second equation, y = -(1/4)x - 9, is -(1/4).
Since the slopes are negative reciprocals of each other (i.e., the product of the slopes is -1), the two equations are perpendicular to each other.