Question

Which situation represents a proportional relationship?

A) The cost of purchasing a basket of oranges for $1.80 per pound plus $5.00 for the basket.
B) The cost of purchasing oranges for $1.50 per pound plus a shipping fee of $0.25 per pound.
C) The cost of purchasing oranges for $1.90 per box of apples with a delivery charge of $3.50.
D) The cost of purchasing oranges for $1.75 per pound with a coupon for $1.00 off the total cost.

Answer 1

option B) The cost of purchasing oranges for $1.50 per pound plus a shipping fee of $0.25 per pound.

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`k=(y)/(x)` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

case A) The cost of purchasing a basket of oranges for $1.80 per pound plus $5.00 for the basket

Let

x ----> the pounds of oranges

y ---> the total cost

The linear equation is equal to

`y=1.80x+5`

The line not passes through the origin (because the y-intercept is not zero)

therefore

This situation not represent a proportional relationship

case B) The cost of purchasing oranges for $1.50 per pound plus a shipping fee of $0.25 per pound

Let

x ----> the pounds of oranges

y ---> the total cost

The linear equation is equal to

`y=(1.50-0.25)x`

`y=(1.25)x`

The line passes through the origin

therefore

This situation represent a proportional relationship

case C) The cost of purchasing oranges for $1.90 per box with a delivery charge of $3.50

Let

x ----> the number of box

y ---> the total cost

The linear equation is equal to

`y=1.90x+3.50`

The line not passes through the origin (because the y-intercept is not zero)

therefore

This situation not represent a proportional relationship

case D) The cost of purchasing oranges for $1.75 per pound with a coupon for $1.00 off the total cost

Let

x ----> the pounds of oranges

y ---> the total cost

The linear equation is equal to

`y=1.75x-1.00`

The line not passes through the origin (because the y-intercept is not zero)

therefore

This situation not represent a proportional relationship