Suppose a real world event occurs at regular intervals such as having a birthday party, renting videos, or driving. How can Algebra help us visualize the past, present, and future of these activities without re-creating the event? Depending on what we need, there are three tools to help us GET more information from the events: (G)raphs, (E)quations, and (T)ables. Tables Equations Graphs MAIN

If you need to keep track of specific values in a list for quick reference such as:  Rental list of Videos vs. Cost (If I rent x videos, then I will be charged y dollars.)  Storage capacity of RAM vs. Time (If I get x amount of RAM, then I can store up to y minutes of music.) 1. Can you think of other lists that would be helpful for quick referencing? 2. How does the slope, y-intercept, and variables of a table relate to graphs and equations? Equations Graphs MAIN Slope y-Intercept Variables

If you need to quickly show a classmate or calculator how a function works but don’t have much paper or time, you need an equation so they can construct a table or graph for you. 1. Can you think of other ways that equations are more useful compared to graphs or tables? 2. How does the slope, y-intercept, and variables of an equation relate to graphs and tables? Tables Graphs MAIN Slope y-Intercept Variables

If you need to visually show a group of people who are mathematically challenged how one variable affects another, you need a graph. 1. Can you think of two variables that would be helpful to show more in a graph rather than a table or equation? 2. How does the slope, y-intercept, and variables of an graph relate to equations and tables? Tables Equations MAIN Slope y-Intercept Variables

Graphs: 1. Pick a Point1 (P1) and a Point2 (P2). 2. The change in y’s (from P1 to P2) is the RISE and the change in x’s (from P1 to P2) is the RUN. 3. Divide the RISE over the RUN. Equations: 1. The coefficient in front of the x variable represents the RISE over the RUN. If only one number is present, the RISE is the number shown and the RUN is 1. Tables: 1. Pick a row to represent Point1 (P1) and another row to represent Point2 (P2). 2. The change in y’s (from P1 to P2) is the RISE and the change in x’s (from P1 to P2) is the RUN. 3. Divide the RISE over the RUN. Tables Equations Graphs MAIN

Graphs: 1. Independent variable is located along the x-axis. 2. Dependent variable is located along the y-axis. Equations: 1. Independent variable is represented by the x. 2. Dependent variable is represented by the y. Tables: 1. Independent variable is usually represented by the first column. 2. Dependent variable is usually represented by the second column. Tables Equations Graphs MAIN

Graphs: 1. The value along the y axis where the line intersects the y-axis. Equations: 1. The sign and number on its own on the right side of the equation. Tables: 1. Pick the row where the first column value is zero. 2. The second column value for the row found in #1. Tables Equations Graphs MAIN