Question

grace is comparing cell phone plans. a prepaid phone plan costs $0.20 per minute and ha contracted phone plan costs $50 per month and $0.02 per minute. how will the graphs 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: Define cost equations

Let $y$ represent total monthly cost.

• Prepaid plan: $y = 0.20x$
• Contracted plan: $y = 0.02x + 50$

Step2: Compare slopes (steepness)

Slope of prepaid: $0.20$; Slope of contracted: $0.02$.
Since $0.20 > 0.02$, prepaid line is steeper.

Step3: Compare y-intercepts

Y-intercept of prepaid: $0$; Y-intercept of contracted: $50$.
Since $0 < 50$, prepaid has lower y-intercept.

Answer:

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