Linear Equations

New Zealand

Level 6 - NCEA Level 1

Lesson

- To visualize different types of slopes and relationships
- To practice applying different functions to real life situations

- Colored Tape
- Deck of Cards (1-10 only)
- 12 Pieces of Paper
- Markers
- Pen
- Scissors

- Use the tape to create a set of axes on the floor. The axes should be about 3 meters long and 3 meters high. You may want to set this up outside.
- On the horizontal axis measure out 30cm from the center on either side and place a tick mark with your tape. Continue placing tick marks every foot along the horizontal axis. When you reach the end of the tape there should be 10 tick marks, 5 on each side.
- Do the same thing for the vertical axis.
- On each piece of tape use your marker to label it appropriately with the numbers: 2,4,6,8,10 or -2,-4,-6,-8,-10.

Work with at least one other person.

- The members in your group should stand on the number plane to model the following relationships:
- Direct proportional
- Inverse proportional
- Linear
- Non Linear

- The members in your group should stand on the number plane to model the following equations:
- y=6x
- y=-2x+2
- y= 3x+5

- You and a partner pick two different points on the grid to stand on.
- Find the slope of the line that would connect where you and your friend stand.
- Find the equation of the line that would connect where you and your friend stand. Write it down.
- One of you take one step upward on the graph. Recalculate the slope and the equation of the line. Write it down.

- How did the slope change when you took a step upward on the graph?
- From your last answer, what observations can you make about the slope of a line?
- How did the change in slope change the equation?
- What method did you use to find the equations of the lines?
- What is the intersection point for the equations of the two lines?
- What are the x and y intercepts for each of the equations of the two lines?
- Out of all of the equations you modeled, which had the steepest slope?
- Pick any two equations that you modeled. Draw a sketch of each and create a scenario that explains the behavior of the graph. Make sure you label the axes of your sketches and title them.
- Share your graphs with a friend. What stories did they come up with? How did they come up with their ideas?