5.1+Graphing+on+a+Calculator+0910

Date: 3, October 2009 Initials: N.A Big Idea: Observation and description of changes in the world around us are the first steps in finding and learning about patterns. Essential Question: How can a graphing calculator help me to discover relationships between variables?

** Problem 5.1: Questions ** ** Experiment with your graphing calculator and the following equations. Graph one set of equations at a time. For each set, 2 of the graphs will be similar in some way, and one of the graphs will be different. Answer question A and B for each **

** Set 1: ** ** y=3x-4, **  **y=x²,**  ** y=3x+2 **

** Set 2: y=5, y=3x, y=1x

Set 3: y=2x+3, y=2x-5, y=0.5x+2

Set 4: y=2x, y=2 ** ** / ** ** x, y=x+5

Question A: 1. Which 2 equations in the set have graphs that are similar? 2. In what ways are the 2 graphs similar? 3. In what ways are the equations for the 2 graphs similar?

Question B: ** ** 1. Which equations in the set has a graph that is different from the graphs of the other equations ? 2. In what way is the graph different from the other graphs? 3. In what way is the equations different from the other equations? ** Answers:

Set 1: Graph:

Green: y=x² Blue: y=3x+2 Red: y=3x-4 A1. y=3x-4 and y=3x+2 have similar graphs.

A2. They are straight lines, they point the same direction and they are parallel

A3. The equations are similar because they contain x as an independent variable with a fixed number 3

B1: y=x² has a different graph from the other two equations.

B2: This graph is not a straight line, its a curve, both of the other graphs are a straight line

B3: This equation contains x² as an independent variable, where as other two equations have x as an independent variable.

Set 2: Graph:

Red: y=5 Green: y=3x Blue: y=1x A1. y=3x and y=1x have similar graphs.

A2. They are straight lines, and both have crossed the 0,0 point in the graph

A3. The equations are similar because they contain x as an independent variable

B1: y=5 has a different graph from the other two equations.

B2: This graph is a straight line, but its not dependent on any other variable.

B3: This equation does not contains x as an independent variable, where as other two equations have x as an independent variable.

Set 3:Graph:

Blue: y=.5x+2 Red: y=2x+3 Green: y=2x-5 A1. y=2x+3 and y=2x-5 have similar graphs.

A2. They are straight lines, they point the same direction and they are parallel

A3. The equations are similar because they contain x as an independent variable and with a fixed number of 2

B1: y=.5x+2 has a different graph from the other two equations.

B2: This graph is a straight line, but its not parallel with the other 2 graphs.

B3: This equation contains x as an independent variable with .5 as an fixed number, where as other two equations have x as an independent variable with 2 as an fixed number

Set 4:Graph:

Green: y=2/x Red: y=2x Blue: y=x+5 A1. y=2x and y=x+5 have similar graphs.

A2. They are straight lines

A3. The equations are similar because they contain x as an independent variable

B1: y=2/x has a different graph from the other two equations.

B2: This graph is not a straight like, its a curve, both of the other graphs are a straight line

B3: This equation contains x as an independent variable, but its not multiplied with the fixed number, rather it divides the fixed number, where as other two equations have x as an independent variable which multiplies with the fixed number.

1 Use the equation y= 2x to answer the following questions a. If x=2, what is y? y=4 b. If x=2/3, what is y? y=4/3 c. If x=3.25, what is y? y=6.5 d. You can make a table to show pairs of numbers that fit an equations. Complete the following table for the equations y=2x** Completed Table: 3. How is the table for y=2x+3 in the question 2 similar to the table for y=2x in question 1?
 * Problem 5.1 Follow Up:
 * x || 0 || 1 || 2 || 3 || 4 || 5 || 6 ||
 * y || 0 || 2 || 4 || 6 || 8 || 10 || 12 ||
 * 2. Complete the following table for the equations y=2x+3**
 * x || 0 || 1 || 2 || 3 || 4 || 5 || 6 ||
 * y || 3 || 5 || 7 || 9 || 11 || 13 || 15 ||

Both the table have same number of column and rows. Both contain the variables x, and y. And for both table the value for x are the same and the value for y slowly progressed from lower to higher value in both of them. In both of them the y variable increased by 2's.