Which equation represents a proportional relationship?
A. Y = 1/4x + 4
B. Y = 1/4x + 1
C. Y = 1/4 x
D. Y = 1 / 4x + 1/4
C. Y = 1/4 x (since the equation has a constant ratio of Y to x, indicating a proportional relationship)
To determine which equation represents a proportional relationship, we need to recall the characteristics of a proportional relationship. In a proportional relationship, the ratio between the two variables (x and y) remains constant.
The equation of a proportional relationship can be written in the form y = kx, where k is the constant of proportionality.
Let's analyze the given options:
A. Y = 1/4x + 4: This equation does not represent a proportional relationship because it includes a constant term (4). In proportional relationships, there should not be any constant term.
B. Y = 1/4x + 1: Similar to option A, this equation has a constant term (1), so it does not represent a proportional relationship.
C. Y = 1/4x: This equation represents a proportional relationship because it follows the form y = kx, where k = 1/4. In this equation, the ratio of y to x is always 1/4.
D. Y = 1/4x + 1/4: Similar to options A and B, this equation includes a constant term (1/4), so it does not represent a proportional relationship.
Therefore, the equation that represents a proportional relationship is C. Y = 1/4x.