*5. A calling card charges \( 50 c \) for each call placed plus 3 e per minute on the call. a. Make a table that lists possible durations of phone calls and the corresponding charges. b. Write an equation for the function. c. Is the function an example of direct variation? Why or why not?

**a. Table of Phone Call Duration vs. Charges** Let \( x \) be the number of minutes of the call and \( C(x) \) be the total charge in cents. The calling card charges a fixed fee of \( 50 \) cents for each call plus \( 3 \) cents for every minute of the call. This gives the calculation: \[ C(x)=50+3x \] Below is a sample table showing a few durations and their corresponding charges: | Minutes (\( x \)) | Charge \( C(x)=50+3x \) (in cents) | |-------------------|--------------------------------------| | 1 | \( 50+3(1)=53 \) | | 2 | \( 50+3(2)=56 \) | | 3 | \( 50+3(3)=59 \) | | 4 | \( 50+3(4)=62 \) | | 5 | \( 50+3(5)=65 \) | **b. Equation for the Function** The equation that represents the charge for a phone call of duration \( x \) minutes is: \[ C(x)=50+3x \] **c. Is the Function an Example of Direct Variation?** A function is an example of direct variation if it can be written in the form: \[ y = kx \] where \( k \) is a constant and there is no additional constant term. In our function \( C(x)=50+3x \), there is a fixed fee of \( 50 \) cents. This means that when \( x=0 \), \( C(0)=50 \) instead of \( 0 \). Thus, the function is **not** an example of direct variation because of the constant term \( 50 \).