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 40 minutes of calls is $12.18 and the monthly cost for 97 minutes is $17.31. What is the monthly cost for 54 minutes of calls?
it was $13.44
sorry molly you're right
i put in calculator 12.18 = .09(4) + b instead of 12.18 = .09(40) + b
To find the monthly cost for 54 minutes of calls, we can use the given information about the linear function.
We are told that the monthly cost (in dollars) is a linear function of the total calling time (in minutes). Let's call the monthly cost "C" and the total calling time "T".
We are given two points on the linear function: (40, 12.18) and (97, 17.31).
The formula for a linear function is:
C = mT + b
Where "m" is the slope of the line and "b" is the y-intercept.
To find the values of m and b, we can use the two given points.
Using the point (40, 12.18):
12.18 = m(40) + b ----(1)
Using the point (97, 17.31):
17.31 = m(97) + b ----(2)
Now we have a system of two equations with two variables (m and b). We can solve this system to find the values of m and b.
Subtracting equation (1) from equation (2):
17.31 - 12.18 = m(97) - m(40) + b - b
5.13 = m(97 - 40)
5.13 = m(57)
m = 5.13/57
m ≈ 0.09
Now substitute the value of m into equation (1) to find b:
12.18 = 0.09(40) + b
12.18 = 3.6 + b
b ≈ 12.18 - 3.6
b ≈ 8.58
So the equation of the linear function is:
C = 0.09T + 8.58
To find the monthly cost for 54 minutes of calls (T = 54), substitute T = 54 into the equation:
C = 0.09(54) + 8.58
C ≈ 13.14
Therefore, the monthly cost for 54 minutes of calls is approximately $13.14.
m (the slope) = (17.31-12.18)/(97-40) = .09
y = mx + b = .09x + b
if i plug a point into the equation, i get b
12.18 = .09(40) + b
b = 11.82
y = .09(54) + 11.82 = $16.68
:)