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

April 28, 2010 TVG

__Big Idea:__ Negative numbers help us to model many real world situations.

__Essential Question:__ How do I multiply and divide integers?

__Notes:__ When multiplying and dividing integers… __ Problem 5.3 Using a Calculator to Explore Lines __ A)
 * Two of the same signs equal a positive answer (+ x + = +, - x - = +)
 * Two different signs equal a negative answer (+ x - = -)

1. Enter the equation y= 4x into your calculator, 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 will differ form the graph of y= 4x. Then, enter the equation y= -4x and press ‘GRAPH’ to see the graphs of both equations in the same window. Add a sketch of y= -4x to you sketch from part 1. I think the graph of the equation y= -4x will be going in the opposite direction of the graph for y= 4x.

3. How are the graphs alike? How are they different?

The graphs are similar because the lines go through the center of the graph at the same point in time but they are different because they go through the opposite numbers 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 play key to see the second column. Copy part of the table onto you paper.

X Y1 Y2
 * = -2 ||= -8 ||= 8 ||
 * = -1 ||= -4 ||= 4 ||
 * = 0 ||= 0 ||= 0 ||
 * = 1 ||= 4 ||= 4 ||

2. For each value of x in the table. Look at the two corresponding values of y (Y1 and Y2). How are the two y values for a given x value related? How does this relationship show up in the graph?

For each value of x both of the y values multiplied by the absolute value of 4. This relationship shows on the graph because each and every point on the y axis line is 4 spaces from the point on the x axis.

C) With you graphing calculator, experiment with each set of equations. Look at the graphs and the tables, Record you observations.

1. y=4x+5 and y=-4x+5 Both of the lines intersect at the same point on the y axis. They meet at 5 because the equation is y=4x**+5** and y=-4x**+5**.

2. y=4x-5 and y=-4x-5 On this graph, the lines meet at -5 because in the equation you are subtracting 5.