Which situation could NOT represent a proportional relationship?

Question 1 options:

The weight in x weeks of a puppy that gains 2 pounds per week if it starting weight is 8 pounds.

The cost of purchasing p pounds of bananas for $0.55 per pound.

The number of gallons of water in x barrels with 50 gallons of water in each barrel

The amount an employee who makes $9.25 per hour earns in h hours

A proportional relationship is one in which one variable varies directly with the other. Let the dependent variable be y and independent variable be y.

If y is directly proportional to x, then,

[tex]y=kx[/tex], where, k is a constant of proportionality.

Now, let us check each option and try to express a relationship between them.

Option 1:

The weight in [tex]x[/tex] weeks of a puppy that gains 2 pounds per week if it starting weight is 8 pounds.

Let the weight be represented by [tex]W[/tex]. Initial weight is 8 pounds.

Weight gain per week is 2 pounds. So, weight gain in [tex]x[/tex] weeks is [tex]2x[/tex].

Therefore, total weight is, [tex]W=8+2x[/tex]

This is a linear relationship but not a proportional relationship as it is not of the form [tex]y=kx[/tex]. So, option 1 could NOT represent a proportional relationship.

Option 2:

Cost of purchasing 1 pound of bananas is $ 0.55. So, cost of purchasing [tex]p[/tex] pounds of bananas will be [tex]C=0.55p[/tex]. It is of the form [tex]y=kx[/tex]. So, it represents a proportional relationship.

Option 3:

Number of gallons of water in 1 barrel is 50. So, number of gallons in [tex]x[/tex] barrels will be [tex]N=50x[/tex]. It is of the form [tex]y=kx[/tex]. So, it represents a proportional relationship.

Option 4:

Amount earned by an employee in 1 hour is $ 9.25. So, amount earned in [tex]h[/tex] hours will be [tex]A=9.25h[/tex]. It is of the form [tex]y=kx[/tex]. So, it represents a proportional relationship.