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.

Answer 1

The answer would be A. or the first one.

Answer 2

Answer:  The prepaid phone plan will have a steeper line and lower y-intercept.

Step-by-step explanation:

Let x represents the number of minutes while y represents total cost of one month,

According to the question, A prepaid phone plan costs $0.20 per minute and has no monthly fee.

Thus, equation of line which shows it,

y = 0.20x  ------- (1)

And,  A contracted phone plan costs $50 per month and $0.02 per minute.

Thus, equation of line which shows it,

y = 50+0.020x -------(2)

Since, After plotting both lines we come to know that the slope of line 1) is greater than 2) therefore line 1) is steeper than 2).

Also, The y-intercept of 1) is (0,0) and y-intercept of 2) is (0,50)

Therefore Line 1) has the lower y-intercept than line 2).

Thus, Option One is correct.