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

5-17-09 M.D Accentuate the Negative


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

5.3 Using a calculator to explore lines 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.

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. Green=-4x 3. How are the graphs alike? And How are they different? The graphs are alike as they are the same absolute value the entire time, from-10 to 10. But they are different as they are opposite each other, and -4x is moving backward in the y coordinate.

1. Press Table to look at the table showing data for both equations. You may need to use the forward key to see the Y2 Collum. 2. For Each value of //x// in the table, look at the two corresponding values of y1 and y2. How are the two y values for a given //x// value related? How does this relationship show up in the graph. The two are related because Y1 is always the same absolute value as Y2 except, Y1 is positive and Y2 is negative. This shows up on a graph by two lines going opposite each other at the exact same angle, and meeting in the center to form an X. 1. y=4x+5 and y=-4x+5. They are opposite each other the whole way, showing that they are the same equations just with one positive one negative.
 * B.**
 * X || **y1 ** ||  y2 ||
 * 0 || 0 || 0 ||
 * 1 || 4 || -4 ||
 * 2 || 8 || -8 ||
 * 3 || 12 || -12 ||
 * 4 || 16 || -16 ||
 * 5 || 18 || -20 ||
 * ** 6 ** || ** 20 ** || ** -24 ** ||
 * C.** With your graphing calculator, experiment with each set of equations. Look at the graphs and the tables. Record your observations.

2. y=4x+5 and y=-4x-5. (Graph couldn’t upload.) It is the same as number one except flipped over. Showing that the plus 5 turned to minus 5.

Follow-Up 1. Y=3x and y=-3x will be opposite each other forming an X in the middle. 2. Y=3x-3 and Y =3x+3 will make slanted parallel lines. 3. Y=3x-3 and Y=-3x-3 will make lines that intersect at the top. 4. Give 3 other pairs of equations that will have a similar relation to the ones above. 1) y=10x and y=-10x 2) Y=10x-10 and Y=10x+10 3) Y=10x-10 and Y=-10x-10
 * Right**
 * Right**
 * Right**