Question

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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 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. the contracted phone plan will have the same steepness and a higher y - intercept.

Explanation:

Step1: Write cost - equations

For the prepaid plan, the cost $y_1$ is given by $y_1 = 0.2x$ (since it's $0.20$ per minute and no monthly fee, so the y - intercept is 0). For the contracted plan, the cost $y_2$ is given by $y_2=50 + 0.02x$, where the y - intercept is 50 and the slope is 0.02.

Step2: Analyze slopes and y - intercepts

The slope of the prepaid plan is $m_1 = 0.2$ and the slope of the contracted plan is $m_2=0.02$. Since $0.2>0.02$, the prepaid plan has a steeper line. The y - intercept of the prepaid plan is 0 and the y - intercept of the contracted plan is 50, so the prepaid plan has a lower y - intercept.

Answer:

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