Acompany 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

To solve this, we are going to use the slope formula, and the point slope formula.
Slope formula: 
where
is the slope.
  are the coordinates of the first point.
  are the coordinates of the first point.
Point-slope formula: 

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:



Now that we have the slope, we can use the point slope formula:




Remember that in a linear equation of the form ,  is the slope and  is the y-intercept. In our model the y-intercept is the membership fee.
Since  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).







Membership fee: $8

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







Membership fee: $5

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







Membership fee: $3

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

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