1. Rates of Change and Initial Values

2. Remember this problem?
FallonMusic.com charges a $19 subscription fee plus $0.10 per download. WellsMusic.com charges a $21 subscription fee plus $0.05 per download.
How many downloads would have to be purchased for the cost of FallonMusic.com to equal the cost of WellsMusic.com?
What equation can you use to solve this word problem?

3. Let’s break down the parts:
FallonMusic.com charges a $19 subscription fee plus $0.10 per download.
What’s the initial value that you have to pay to get music?
What’s the rate that you pay?

4. Now for the other expression:
WellsMusic.com charges a $21 subscription fee plus $0.05 per download.
What’s the initial value that you have to pay to get music?
What’s the rate that you pay?

5. Let x = number of downloads
We found on the test that the solution to the equation was 40 downloads.
Plug this back in to each expression. What value do you get?
What does this number represent in the problem?

6. Say “hello” to y
The two things that we don’t know for each music service are the number of downloads and the total cost of the service.
That is why we have two variables:
x = number of downloads
y = total cost of the service

7. FallonMusic.com In words: As an equation:
The total cost of the FallonMusic.com service is equal to $0.10 per download plus a $19 subscription fee.
As an equation:
y = 0.10x + 19

8. WellsMusic.com In words: As an equation:
The total cost of the WellsMusic.com service is equal to $0.05 per download plus a $21 subscription fee.
As an equation:
y = 0.05x + 21

9. You just wrote your first two linear equations!
A linear equation is an equation whose x- and y- values change at the same rate throughout the graph.
It’s called linear because the points make a line.
Whenever a set of values are growing at a constant rate (slope), they form a line and are thus linear.

10. Group Work Time!
You have 2 minutes to read your situation, fill out the information and write a linear equation.
When the timer goes off, take turns sharing what your wrote.
Teammates, listen, tell the person who is sharing if you agree or disagree and why, and then write down the information.
Do not do other problems by yourself…don’t steal
your teammates’ thunder!