Question

Which of the equations below represent proportional relationships? If the relationship is proportional, identify the constant of proportionality. If the relationship is not proportional, explain why.

a) (y = 2x)
b) (y = 1/3x)
c) (y = x^2)
d) (y = 4/5x)

Answer 1

Equations a) y = 2x, b) y = 1/3x, and d) y = 4/5x represent proportional relationships with constants of proportionality of 2, 1/3, and 4/5 respectively. Equation c) y = x^2 is not proportional as it represents a quadratic relationship.

Step-by-step explanation:

To determine whether the relationships described by the given equations are proportional, we can check if they are of the form y = kx, where k is the constant of proportionality. An equation that represents a proportional relationship will result in a straight line passing through the origin when plotted.

• a) y = 2x: This equation represents a directly proportional relationship with a constant of proportionality of 2.
• b) y = 1/3x: This equation is also directly proportional with a constant of proportionality of 1/3.
• c) y = x^2: This equation does not represent a proportional relationship because the relationship between y and x is quadratic, not linear. Therefore, it does not follow the form y = kx.
• d) y = 4/5x: This equation is directly proportional with a constant of proportionality of 4/5.

The equations labeled a), b), and d) portray linear relationships with their respective constants of proportionality, while equation c) is not proportional since it's quadratic.