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 \( y\) of the prepaid plan is \( y = 0.2x\) (since \( m = 0.2\) and \( b=0\)). The cost \( y\) of the contracted plan is \( y=0.02x + 50\) (where \( m = 0.02\) and \( b = 50\)).

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

The slope of the prepaid plan (\(m_{prepaid}=0.2\)) is greater than the slope of the contracted plan (\(m_{contracted}=0.02\)). A larger slope means a steeper line. The \(y\) - intercept of the prepaid plan (\(b_{prepaid}=0\)) is less than the \(y\) - intercept of the contracted plan (\(b_{contracted}=50\)).

Answer:

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