From Functions of Lines to Graphs of Lines
Problem 1: Desmond's Ipod
Instructions for problem: You may work with a partner or in groups of three on this problem. After some time, we will discuss the problem as a class. Try to think in terms of x’s and y’s – the coordinate’s in ordered pairs, and using x and y as a variable.
Desmond likes his Ipod. His tastes in music are as varied from Tupac to Coldplay. Desmond is also a good kid as he helps around the house. His parents have decided to reward him for his helpfulness and have decided to let him purchase two songs on Itunes a day. Desmond would like a way to figure out how many songs he should have after each day. While Demond already has songs on his Ipod, he is only interested in tracking how many new songs we will get when his parents start giving him the money for the songs.
1. Desmond first decides to create an equation to decide how many new songs he should have on a given day. What equation would help to describe how many new songs Desmond will have after a certain amount of days? Use two variables in your equation.
2. Great! We have an equation. Good job. Now to execute phase 2 and figure out a way to create a graph based on this equation we’ve made for Desmond. How can we go from this equation to a graph? How might each variable be useful in making ordered pairs? Create the graph on a grid with a y-axis and an x-axis.
Activity: Class Discussion
Now that we have had some time to think about the equation we created for Desmond and it's relation to a graph, let's discuss the connection between equations and graphs.
Problem 2: Chuck's Funds
Instructions for problem: You may work with a partner or in groups of three on this problem. After some time, we will discuss the problem as a class. Try to think in terms of x’s and y’s – the coordinate’s in ordered pairs, and using x and y as a variable.
A wealthy man named Charles Widmore has many bank accounts which he uses to fund his business ventures. Charles has put 20,000 in one of these bank accounts, and uses it regularly to pay off a loan he acquired to pay for one of his buildings. He pays 1,000 dollars a month. Mr. Widmore would like to know how much money he will have in his bank account at any time, so he has some of his accountants draw the graph.
1. Find an equation which can be used to compute how much money Mr. Whitmore will have during any month. Use two variables in your equation.
2. Mr. Widmore asked for a graph, so let us do our job and make a graph of the equation we found in part 1. What should we use as a scale for this graph?
Activity: Class Discussion
How is this graph different from the graph we made for Desmond?
Reflection
What is the relationship between graphs of lines and functions of lines? What have you learned?