Linear Equations

NZ Level 6 (NZC) Level 1 (NCEA)

Life Size Line Graphs (Investigation)

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$2,4,6,8,10 or $-2,-4,-6,-8,-10$−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`=6`x` - $y=-2x+2$
`y`=−2`x`+2 - $y=3x+5$
`y`=3`x`+5

- $y=6x$
- 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?

Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns

Apply algebraic procedures in solving problems