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

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

Since \(0.2>0.02\), the prepaid plan has a steeper slope. And \(b_1
eq b_2\) ( \(0
eq50\)).

Answer:

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