grace is comparing cell phone plans. a prepaid phone plan costs $0.20 per minute and has no monthly fee. a…

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?\nthe prepaid phone plan will have a steeper line and lower y - intercept.\nthe contracted phone plan will have the same steepness and a higher y - intercept.\nthe prepaid phone plan will have a less steep line and the same y - intercept.\nthe contracted phone plan will have a steeper line and same y - intercept.

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?\nthe prepaid phone plan will have a steeper line and lower y - intercept.\nthe contracted phone plan will have the same steepness and a higher y - intercept.\nthe prepaid phone plan will have a less steep line and the same y - intercept.\nthe contracted phone plan will have a steeper line and same y - intercept.

Answer

Explanation:

Step1: Write cost - equations

The cost $y_1$ of the prepaid plan is $y_1 = 0.2x$ (since it's $0.2$ dollars per minute and no monthly fee). The slope $m_1=0.2$ and the $y$-intercept $b_1 = 0$. The cost $y_2$ of the contracted plan is $y_2=50 + 0.02x$, where the slope $m_2 = 0.02$ and the $y$-intercept $b_2=50$.

Step2: Compare slopes and y - intercepts

Comparing slopes, $m_1=0.2$ and $m_2 = 0.02$, and $0.2>0.02$, so the prepaid - plan line is steeper. Comparing $y$-intercepts, $b_1 = 0$ and $b_2=50$, so the prepaid - plan has a lower $y$-intercept.

Answer:

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