Question

1. movies an online dvd rental company charges $15 a month for unlimited rentals. determine whether the total paid after each month is proportional to number of months by graphing on the coordinate plane. explain your reasoning. online dvd rentals (graph with x-axis as month (0 - 10) and y-axis as cost ($) (0 - 60))

Explanation:

Step1: Define variables and function

Let \( x = \text{number of months} \), \( y = \text{total cost (\$)} \). The function is \( y = 15x \).

Step2: Identify proportionality condition

Proportional relationships satisfy \( y = kx \) (pass through origin). Here, when \( x=0 \), \( y=0 \) (no cost for 0 months).

Step3: Check graph characteristics

Plot points: (0,0), (1,15), (2,30), etc. The line passes through the origin and has constant slope \( k=15 \).

Answer:

The total paid is proportional to the number of months. The relationship follows \( y = 15x \), a proportional function whose graph passes through the origin with a constant ratio of cost to months (\$15 per month).