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vodomira [7]
3 years ago
6

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 linea

r 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
Mathematics
2 answers:
Luba_88 [7]3 years ago
6 0
To solve this, we are going to use the slope formula, and the point slope formula.
Slope formula: m= \frac{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= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}
m= \frac{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= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}
m= \frac{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= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}
m= \frac{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= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}
m= \frac{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 <span>Plan D.</span> 


frozen [14]3 years ago
5 0

Answer:

Your answer is Plan D

Step-by-step explanation:

HOPE IT HELPS

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