Question

A company offers four plans for customers who want to rent DVDs and video games. The cost of the plans can be modeled by a linear function that combines a one time membership fee with a per disc rental rate. The table shows the total cost, including membership fees, for a person who rents 1,2 and 5 discs in a month

Discs rented plan A B C D
1. $14. $12. $10. $12
2. $17. $16. $15. $21
5. $26. $28. $30. $48



Which plan has the smallest one-time membership fee?
Plan A
Plan B
Plan C
Plan D

Answer 1

Your answer is Plan D

Explanation:

HOPE IT HELPS

Answer 2

To solve this, we are going to use the slope formula, and the point slope formula.
Slope formula:
`m= (y_(2)-y_(1))/(x_(2)-x_(1))`
where

`m` is the slope.

`(x_(1),y_(1))` are the coordinates of the first point.

`(x_(2),y_(2))` are the coordinates of the first point.
Point-slope formula:
`y-y_(1)=m(x-x_(1))`

Plan A. Coordinates of the first point: (1,14) (number of discs, cost). Coordinates of the second point: (2,17). Lets replace those values in our slope formula:

`m= (y_(2)-y_(1))/(x_(2)-x_(1))`

`m= (17-14)/(2-1)`

`m=3`
Now that we have the slope, we can use the point slope formula:

`y-y_(1)=m(x-x_(1))`

`y-14=3(x-1)`

`y-14=3x-3`

`y=3x+11`
Remember that in a linear equation of the form
`y=mx+b`,
`m` is the slope and
`b` is the y-intercept. In our model the y-intercept is the membership fee.
Since
`b=11` in our linear equation, we can conclude that the membership fee is $11

Plan B. Coordinates of the first point (1,12). Coordinates of the second point (2,16).

`m= (y_(2)-y_(1))/(x_(2)-x_(1))`

`m= (16-12)/(2-1)`

`m=4`

`y-y_(1)=m(x-x_(1))`

`y-12=4(x-1)`

`y-12=4x-4`

`y=4x+8`
Membership fee: $8

Plan C. Coordinates of the first point: (1,10). Coordinates of the second point: (2,15).

`m= (y_(2)-y_(1))/(x_(2)-x_(1))`

`m= (15-10)/(2-1)`

`m=5`

`y-y_(1)=m(x-x_(1))`

`y-10=5(x-1)`

`y-10=5x-5`

`y=5x+5`
Membership fee: $5

Part D. Coordinates of the first point: (1,12). Coordinates of the second point (2,21).

`m= (y_(2)-y_(1))/(x_(2)-x_(1))`

`m= (21-12)/(2-1)`

`m=9`

`y-y_(1)=m(x-x_(1))`

`y-12=9(x-1)`

`y-12=9x-9`

`y=9x+3`
Membership fee: $3

We can conclude that the plan that has the smallest one-time membership is Plan D.