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 monthly 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.

Explanation:

Step1: Define Cost Functions

For the prepaid plan: \( y = 0.20x \) (slope \( m_1 = 0.20 \), y - intercept \( b_1 = 0 \)).
For the contracted plan: \( y = 0.02x + 50 \) (slope \( m_2 = 0.02 \), y - intercept \( b_2 = 50 \)).

Step2: Compare Slopes (Steepness)

Since \( 0.20>0.02 \), the prepaid plan has a steeper line (larger slope means steeper).

Step3: Compare Y - Intercepts

Prepaid y - intercept: \( 0 \); Contracted y - intercept: \( 50 \). So prepaid has a lower y - intercept.

Answer:

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