Question

On the Talk for Less long-distance phone plan, the relationship between the number of minutes a call lasts, and the cost of the call, is linear. A 5-minute call costs $1.25, and a 15-minute call costs $2.25. How do you show this in an equation?

Answer 1

the equation is
C `=` $`0.10` `x` +``$`0.75`

Explanation:

This is a linear function question.
It uses the slope-intercept form of linear equations
`y = mx + b`

By looking at the data, you can tell that this is not a simple "cost per minute" function.
So there must be a fixed fee added to the "per minute" cost for each call.

The fixed cost per call is applied no matter how long the call lasts.
If you talk for 1 minute or 100 minutes -- or even for 0 minutes -- you are still charged a fixed fee just to make the call.

Then the number of minutes is multiplied by the cost per minute, which naturally varies for each call length.

Then the total cost of all the minutes is added to the fixed fee to reach the final total cost of the call.
............

You can figure out the fixed starting fee by comparing the two given calls.

Both calls must include the fixed fee one time each, after which the per minute charges were applied.

That means that the entire difference in cost between the 5-minute call and the 15-minute call must be due to the extra ten minutes.

For 15 minutes, the amount came to $2.25
For   5 minutes, the amount came to $1.25

Therefore, the extra 10 minutes cost $1.00, which is 10ȼ a minute.
This is the per minute cost of making a call.
The "fixed fee* cost is hidden in the rest of the cost.

A five-minute call @ 10ȼ per minute = 50ȼ
So the rest of the charge must be the fixed fee per call.
$1.25 - $0.50 = $0.75 `larr` the per-call fixed fee.

Check
15 minutes @ 10ȼ per minute . . . . . . . . .$1.50
1 per-call fixed fee @ $0.75 per call . . . $0.75
..........................................................................................
Total charge for a 15-minute call . . . . . .$2.25 Check!

So the equation for this relationship is
`y = mx + b`
where
`y =` total cost of the call, C
`m =` the per minute cost ($0.10 each minute)
`x =` the number of minutes (varies with each call)
`b =` the fixed per-call cost ($0.75 each call)

So the equation is
C `=` $`0.10` `x` +``$`0.75`

This equation means that a call costs 10ȼ a minute
plus one 75ȼ charge per call. .