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: Find the equations of the two plans

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

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

Since \(0.2>0.02\), the prepaid plan has a steeper line (because the slope of a line \(y = mx + b\) determines its steepness, and a larger \(|m|\) means a steeper line).
Since \(0<50\), the prepaid plan has a lower \(y-\)intercept.

Answer:

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