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

Explanation:

Step1: Write cost - equations

The cost $y_1$ of the prepaid plan is $y_1 = 0.2x$ (since it's $0.20$ per minute with no monthly fee, and the slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept, here $m = 0.2$ and $b = 0$). The cost $y_2$ of the contracted plan is $y_2=0.02x + 50$, where the slope $m = 0.02$ and the y - intercept $b = 50$.

Step2: Compare slopes and y - intercepts

The slope of the prepaid plan ($0.2$) is greater than the slope of the contracted plan ($0.02$), so 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.