Question

question
a cell phone carrier charges a fixed monthly fee plus a constant rate for each minute used. in january, the total cost for 250 minutes was $55 while in february, the total cost for 150 minutes was $53.
choose the formula below which gives the function ( c(x) ) representing the monthly cost, in dollars, of a cell phone using ( x ) minutes.
select the correct answer below:
( \bigcirc c(x)=0.02 x+50 )
( \bigcirc c(x)=-0.02 x+56 )
( \bigcirc c(x)=0.05 x+28 )
( \bigcirc c(x)=-0.05 x+78 )

Explanation:

Step1: Calculate the rate (slope)

The rate \(m\) (slope) of the linear function \(C(x)=mx + b\) (where \(x\) is the number of minutes, \(m\) is the rate per minute, and \(b\) is the fixed - fee) can be calculated using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(150,53)\) and \((x_2,y_2)=(250,55)\). Then \(m=\frac{55 - 53}{250 - 150}=\frac{2}{100}=0.02\).

Step2: Find the fixed - fee (y - intercept)

Substitute \(m = 0.02\), \(x = 150\), and \(y = 53\) into the equation \(y=mx + b\). We get \(53=0.02\times150 + b\). First, calculate \(0.02\times150 = 3\). Then the equation becomes \(53=3 + b\). Solving for \(b\), we subtract 3 from both sides: \(b=53 - 3=50\).

Answer:

\(C(x)=0.02x + 50\)