Graphing Exploration

Today we will do a graphing exploration. You learned how to use an online graphing calculator and now I want you to use those skills to complete the following problems.

1. Using your graphing calculator, graph the equations below on the same graph. Sketch these lines on your paper. Use different colors for each line.

y = x

y = 2x

y = 3x

y = 4x

2. What do you notice about the lines? How does changing the number in front of the x change the graph? Write your response on your graph paper under the graphs you sketched.

3. Set up a new x, y axis on your paper. Use the graphing calculator to graph the equations below on the same graph using a different color for each equation.

y = -x

y = -2x

y = -3x

y = -4x

4. On your graph paper explain how these graphs are different than the first set. 

5. The second set of equations have negative coefficients. What can you conclude about graphs with negative numbers in front of the x?

6. On your paper, set up a new x, y axis. Use the graphing calculator to graph the equations below on the same graph using a different color for each equation.

y = x+2

y = x+5

y = x+1

y = x-2

7. Look at your graphs. You notice the numbers in front of the x don’t change but the numbers we add to the x changes. What can you conclude about the graph and the number you add or subtract in the equation?

8. The y intercept form of an equation is:

y=mx + b

The m is the slope and the b is the y intercept. So for an equation like

y=3x-2

I can say that the line will go up in a positive direction because 3 is positive and the line will cross the y axis at -2. I would say the slope is 3 and the y intercept is -2.

y=3x-2

slope: 3

y intercept: -2

Copy all information from number 8 into your notes.  

9. For the following equations, copy the equation then tell the slope and y intercept.

 y = 2x+5

y = -4x -2

y = 1/2x+8

y = 5

y = -5x-4

y = -3x

y = -3/4x + 2

y = 7

 

10. Pick one of the equations above. Create a t-table and graph the line.

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