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 contracted phone plan will have the same steepness and a higher $y$-intercept. the prepaid phone plan will have a steeper line and lower $y$-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 cost - function for prepaid plan

The cost $y_1$ of the prepaid plan with no monthly fee and $0.20$ per minute is given by the equation $y_1 = 0.2x+0$, where the slope $m_1 = 0.2$ and the $y$ - intercept $b_1=0$.

Step2: Find cost - function for contracted plan

The cost $y_2$ of the contracted plan with a $50$ - dollar monthly fee and $0.02$ per minute is given by the equation $y_2=0.02x + 50$, where the slope $m_2 = 0.02$ and the $y$ - intercept $b_2 = 50$.

Step3: Compare slopes and y - intercepts

Since $m_1=0.2$ and $m_2 = 0.02$, and $0.2>0.02$, the prepaid plan has a steeper line. Also, since $b_1 = 0$ and $b_2=50$, the prepaid plan has a lower $y$ - intercept.

Answer:

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