CCN Linear Relationship Equation Initial Condition & the Rate of Change Discussion

Initial Post Instructions

Have you ever ridden a bike uphill? Have you ever skied down a mountain? If so, you know what slope is all about! “Rate of change” is just a way of asking for the slope in a real-world problem; that is the focus of this discussion.

For example, say your current cable bill is $100 plus $10 for every Pay-Per-View movie that you rent during the billing period. The model for your cable bill is as follows: 

• y = 10x + 100, where x = number of Pay-Per-View movies

What is the rate of change? The rate of change or slope is 10. The constant is 100, which is the initial amount that you have to pay even if no Pay-Per-View movies were rented.

For the initial post, address the following:

• Create a linear relationship (equation) that you would use or rely on in your field or everyday life.
• Explain what the linear equation is used for in context of the application.
• Identify the initial condition, such as your initial bill, and the rate of change. For a linear equation, the rate of change (slope).