Which linear equation represents a proportional relationship?
Responses
A y = 3x + 0.2
B y = x + 2
C y = −3x + 4
D y = −0.3x
D y = −0.3x
The linear equation that represents a proportional relationship is D) y = -0.3x. A proportional relationship can be represented by an equation in the form y = kx, where k is the constant of proportionality. In this case, the constant of proportionality is -0.3, which means that for every unit increase in x, y will decrease by 0.3.
To determine which linear equation represents a proportional relationship, we need to identify the equation that can be written in the form y = kx, where k is a constant.
Let's examine each option:
A) y = 3x + 0.2: This equation includes a constant term (0.2) that is not multiplied by x. Therefore, it is not in the form y = kx and does not represent a proportional relationship.
B) y = x + 2: Similarly, this equation has a constant term (2) that is not multiplied by x, so it is not in the form y = kx. It also does not represent a proportional relationship.
C) y = -3x + 4: In this equation, the coefficient of x is -3, which is multiplied by x. However, a proportional relationship equation would have a constant coefficient, not a changing coefficient. Therefore, this equation does not represent a proportional relationship.
D) y = -0.3x: In this equation, the coefficient of x is -0.3, which is a constant value. It is multiplied by x, and there are no additional constant terms. This equation is in the form y = kx, where k = -0.3. Therefore, this equation represents a proportional relationship.
So, the linear equation that represents a proportional relationship is D) y = -0.3x.