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: Write the cost equations

The cost \( y\) for the prepaid plan is \( y = 0.2x+0\) (slope \(m_1 = 0.2\), \(y\)-intercept \(b_1=0\)).
The cost \( y\) for the contracted plan is \( y=0.02x + 50\) (slope \(m_2=0.02\), \(y\)-intercept \(b_2 = 50\)).

Step2: Compare slopes and \(y\)-intercepts

Since \(0.2>0.02\) (so prepaid plan has steeper slope) and \(0<50\) (prepaid plan has lower \(y\)-intercept).

Answer:

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