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,

$y=kx$ , 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 $x$ weeks of a puppy that gains 2 pounds per week if it starting weight is 8 pounds.

Let the weight be represented by $W$ . Initial weight is 8 pounds.

Weight gain per week is 2 pounds. So, weight gain in $x$ weeks is $2x$ .

Therefore, total weight is, $W=8+2x$

This is a linear relationship but not a proportional relationship as it is not of the form $y=kx$ . 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 $p$ pounds of bananas will be $C=0.55p$ . It is of the form $y=kx$ . So, it represents a proportional relationship.

Option 3:

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

Option 4:

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

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3 years ago