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 contracted phone plan will have a steeper line and the same y - intercept. the prepaid phone plan will have a less steep line and the same y - intercept. the prepaid phone plan will have a steeper line and lower y - intercept.

Explanation:

Step1: Write cost - equations

Let $x$ be the number of minutes used in a month. For the contracted phone plan, the cost $y_1$ is given by the equation $y_1 = 50+0.02x$ (a fixed monthly fee of $50$ plus $0.02$ per minute). For the prepaid phone plan, the cost $y_2$ is given by the equation $y_2=0.20x$ (no monthly fee, just $0.20$ per minute).

Step2: Analyze slope and y - intercept

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For $y_1 = 50+0.02x$, the slope $m_1 = 0.02$ and the y - intercept $b_1 = 50$. For $y_2=0.20x$, the slope $m_2 = 0.20$ and the y - intercept $b_2 = 0$. Since $m_2=0.20>m_1 = 0.02$, the prepaid plan has a steeper line (higher rate per minute), and since $b_1 = 50$ and $b_2 = 0$, the prepaid plan has a lower y - intercept.

Answer:

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