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 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: 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, so the slope $m_1=0.2$ and $y$-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

Since $0.2>0.02$, the slope of the prepaid - plan line is steeper.

Step3: Compare y - intercepts

$b_1 = 0$ and $b_2 = 50$, so the $y$-intercept of the prepaid plan is lower.

Answer:

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