# Grace is comparing cell phone plans. A prepaid phone plan costs \$0.20 per minute and has no monthly fee. A contracted phone plan costs \$50 per month and \$0.02 per minute. How will the graphs of the monthy costs of the two cell phone plans compare where x represents minutes purchased in a month?

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## Question:

Grace is comparing cell phone plans. A prepaid phone plan costs \$0.20 per minute and has no monthly fee. A contracted phone plan costs \$50 per month and \$0.02 per minute. How will the graphs of the monthy costs of the two cell phone plans compare where x represents minutes purchased in a month?The prepaid phone plan will have a steeper line and lower y-intercept.
The contracted phone plan will have the same steepness and a higher y-intercept.
The prepaid phone plan will have a less steep line and the same y-intercept.
The contracted phone plan will have a steeper line and same y-intercept.

The prepaid and the contracted plans are illustrations of linear functions, where the prepaid phone plan has a steeper line and lower y-intercept.

We have:

Prepaid

Contracted

For both plans, the cost function (y) is:

Where:

Number of minutes

Steepness

So, we have:

The y intercept (i.e. when x = 0) is

• The steep of the function is 0.20
• The y-intercept is 0

The y intercept is:

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• The steep of the function is 0.02
• The y-intercept is 50

By comparing the steepness and the y-intercepts,

• The prepaid plan is steeper (0.20 > 0.02)
• The prepaid plan has a smaller y-intercept (0 < 50)

Hence, (a) is correct

See attachment for the graphs of both plans