SOLUTION: The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 34 minutes of calls is $12.47 and the

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Question 449356: The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 34 minutes of calls is $12.47 and the monthly cost for 51 minutes is $14.00. What is the monthly cost for 47 minutes of calls?
Answer by lwsshak3(11628) (Show Source):
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The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 34 minutes of calls is $12.47 and the monthly cost for 51 minutes is $14.00. What is the monthly cost for 47 minutes of calls.
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The standard form for a linear or straight-line function is: y=mx+b, where m=slope, and b, the y-intercept. Since you have two points of the function, you are able to find the slope m= ∆y/∆x.
For given problem:
m=(14.00-12.47)/(51-34)=1.53/17
The equation can now be written: y=(1.53/17)x+b
To complete the equation we need to find b.
Plug in the (x,y) values from one of the given points and solve for b
14=51(1.53/17)+b
b=14-51(1.53/17)=9.41
You now have an equation to calculate the monthly cost for any number of calling minutes:
y=1.53x/17+9.41
For 47 minutes of calls,
y=1.53*47/17+9.41=13.64
ans:
For 47 minutes of calling the monthly cost is $13.64
see the graph of this straight-line function below
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