grace is comparing cell phone plans. a prepaid phone plan costs $0.20 per minute and has no monthly fee. a…

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.

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.

Answer

Explanation:

Step1: Escribir ecuaciones para cada plan

Para el plan prepago, el costo mensual $y_1$ se expresa como $y_1 = 0.2x$ (ya que es $0.20$ dólares por minuto y no hay tarifa mensual fija, es decir, la pendiente $m_1=0.2$ y el intercepto $y -$ $b_1 = 0$). Para el plan contratado, el costo mensual $y_2$ se expresa como $y_2=50 + 0.02x$, donde la pendiente $m_2 = 0.02$ y el intercepto $y -$ $b_2=50$.

Step2: Comparar pendientes

La pendiente representa la "pendiente" de la línea. Sabemos que $m_1 = 0.2$ y $m_2=0.02$. Como $0.2>0.02$, la línea del plan prepago es más empinada.

Step3: Comparar interceptos $y -$

El intercepto $y -$ del plan prepago $b_1 = 0$ y el intercepto $y -$ del plan contratado $b_2 = 50$. Entonces, el plan prepago tiene un intercepto $y -$ más bajo.

Answer:

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