5.3+Using+a+Calculator+to+Explore+Lines+0910

5/10/10 L.T. Accentuate the Negative


 * Big Idea: Negative number help us to model many real world situations.**
 * Essential question: How can I add integers**

__Notes:__ Linear equations are equations that have a variable. The graphs form lines. Example: Linear equations: y=4x The graph will look like this.
 * What are linear equations?**

A coordinate grid is divided into 4 sections. This is called quadrants. If the x and y axes are both positive the coordinate point will be in quadrant 1. If the x axe is negetive and y axes is positive then the coordinate point will be in quadrant 2. If both the x and y axes are negetive, it will be in the 3rd axes. If the x axes is positive and y axes is negetive, the coordinate point will go in the 4th axes.
 * What are quadrants?**

a. 1) Enter the Equation y=4x into your graphing calculator as Y1, and then press Graph to see a graph of the equation. Make a Sketch of the Graph you see.
 * __Lesson 5.3__**

a. 2) Predict how the graph of y=-4x would look like, and the difference from y=4x. Then enter the equation in Y2, and press GRAPH to see the graphs of both equations in the same window. Add a sketch of y=-4x to your sketch of part 1. -> I think that the line will go through quadrants 2 and 4 instead of quadrants 1 and 3.

a. 3) How are these graphs alike and how are they different? ->They are alike because no matter what the opposite of the number will have the same absolute value. They are different because they are in different quadrants and they are opposites of each other.

b. 1) Press TABLE to look at the table showing data for both equations (y=4x and y=-4x). You may need to use the [non-computable symbol] (looks like the play button on a DVD remote) key to see the Y2column. Copy part of the table onto your paper. y=-4x
 * x-value || y-value ||
 * -5 || -20 ||
 * -4 || -16 ||
 * -3 || -12 ||
 * -2 || -8 ||
 * -1 || -4 ||
 * 0 || 0 ||
 * 1 || 4 ||
 * 2 || 8 ||
 * 3 || 12 ||

y=4x b. 2) For each value of x in the table, look at the two corresponding values of y (Y1and Y2). How are the two y values for a given x value related? How does this relationship show up in the graph? ->When the x value is the same, the y value is the complet opposite. They have the same absolue value. This is shown in the graphs because if you hold one graph by the mirror, you will see the reflection. They are the same but in different directions.
 * x-value || y-value ||
 * -5 || 20 ||
 * -4 || 16 ||
 * -3 || 12 ||
 * -2 || 8 ||
 * -1 || 4 ||
 * 0 || 0 ||
 * 1 || -4 ||
 * 2 || -8 ||
 * 3 || -12 ||