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 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 equation for the prepaid plan is \(y = 0.2x\) (since \(b = 0\) and \(m=0.2\)). The cost equation for 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 (\(m_1=0.2\)) is steeper than the slope of the contracted plan (\(m_2 = 0.02\)) because \(0.2>0.02\). The \(y\) - intercept of the prepaid plan (\(b_1 = 0\)) is lower than the \(y\) - intercept of the contracted plan (\(b_2=50\)).

Answer:

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