QuestionCompare the cost graphs of a prepaid plan at \x$ minutes.
Studdy Solution
STEP 1
Assumptions1. The prepaid phone plan costs per minute and has no monthly fee.
. The contracted phone plan costs per month and per minute.
3. The variable represents the number of minutes purchased in a month.
STEP 2
We can represent the cost of each plan as a function of , the number of minutes purchased in a month.
For the prepaid plan, the cost is per minute, so the function is .
For the contracted plan, the cost is per month plus per minute, so the function is .
STEP 3
The slope of the line representing each function is the cost per minute.For the prepaid plan, the slope is .
For the contracted plan, the slope is .
STEP 4
The -intercept of the line representing each function is the fixed monthly cost.
For the prepaid plan, the -intercept is because there is no monthly fee.
For the contracted plan, the -intercept is because the monthly fee is .
STEP 5
Comparing the slopes, we see that the prepaid plan has a steeper line ().
Comparing the -intercepts, we see that the contracted plan has a higher -intercept ().
Therefore, the prepaid phone plan will have a steeper line and lower -intercept, and the contracted phone plan will have a less steep line and a higher -intercept.
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