Question

Alyssa has a cell-phone plan that charges a fixed price for each text message, no matter how many she sends. The table below shows the number of text messages Alyssa sent and the amounts she was charged for them on her last three bills.

Using x for the number of text messages sent and y for the amount charged, find the equation of the line that models this relationship and find the rate Alyssa is charged for each text message.

The equation of the line is:

Alyssa is charged_____________for each text message.

Answer 1

Explanation:

Let x represent the number of text messages that Alyssa sent.

Let y for the total amount charged for x messages sent.

Looking at the table showing her last 3 bills,

Total amount charged for 256 messages is $38.40. Charge per text message = 38.4/256 = $0.15

Total amount charged for 177 messages is $26.55. Charge per text message = 177/26.55 = $0.15

Total amount charged for 209 messages is $31.35. Charge per text message = 209/31.35 = $0.15

The charge is constant.

Therefore,

The slope, m = 0.15

Therefore, the equation of the line is

y = mx + c

Intercept, c = 0. The equation becomes

y = 0.15x

Alyssa is charged $0.15 for each text message.