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

[tex]Rate = 0.20[/tex]

[tex]Monthly = 0[/tex]

Contracted

[tex]Monthly = 50[/tex]

[tex]Rate = 0.02[/tex]

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

[tex]y =Monthly + Rate \times x[/tex]

Where:

[tex]x \to[/tex] Number of minutes

[tex]Rate \to[/tex] Steepness

So, we have:

Prepaid

[tex]y =0 + 0.20 \times x[/tex]

[tex]y =0.20x[/tex]

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

[tex]y = 0.20 \times 0 = 0[/tex]

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

Contracted

[tex]y = 50 + 0.02 \times x[/tex]

[tex]y = 50 + 0.02x[/tex]

The y intercept is:

[tex]y = 50 + 0.02 \times 0 = 50[/tex]

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

Read more about linear equations at:

https://brainly.com/question/11897796