Question

A cell phone plan charges $45.50 a month, plus $0.05 per text message. Write and graph an expression to find how many text messages, x, can be sent while still keeping the monthly bill under $60.​

Answer 1

289 messages

equation:
`y=0.05x+45.5`

graph: attached below

Explanation:

We can write this in slope-intercept form, or
`y=mx+b`. Since x is defined as the #of text messages, and 0.05 is the cost of a text message, 0.05 will be m. 45.5 is the base price, or the y-intercept, so it will be b.

Plugging in these numbers, we get
`y-0.05x+45.5`

now we make y = 60, since that is the total amount they have

`60=0.05x+45.5\\14.5=0.05x\\x=290`

So, they can send 290 messages for 60, but they need the bill under 60, so 1 text message less will be 289, and that's enough.