Questions: A basic KouTube TV membership has an activation fee of 45 dollars, plus 70 dollars per month. What linear function represents the total cost of a basic VouTube TV membership for m months? What is the cost for an entire year of service?

To solve this problem, we need to create a linear function that represents the total cost of a basic KouTube TV membership for \( m \) months. The function will include a fixed activation fee and a monthly fee. Then, we will calculate the cost for an entire year (12 months) using this function.

1. Define the linear function for the total cost, which includes the activation fee and the monthly fee.
2. Substitute \( m = 12 \) to find the cost for an entire year.

La función lineal que representa el costo total de una membresía básica de KouTube TV para \( m \) meses se define como: \[ C(m) = 45 + 570m \] donde \( 45 \) es la tarifa de activación y \( 570 \) es la tarifa mensual.

Para encontrar el costo de un año de servicio, sustituimos \( m = 12 \) en la función: \[ C(12) = 45 + 570 \times 12 \] Calculando esto, obtenemos: \[ C(12) = 45 + 6840 = 6885 \]

El costo total para un año de servicio es: \[ \boxed{6885} \]