Linear Equations

NZ Level 6 (NZC) Level 1 (NCEA)

Stepping across the country (Investigation)

Lesson

- To practice creating linear equations to model real life situations.
- To practice finding slope and intercepts.

- Stopwatch
- Pen and Paper
- Internet
- Measuring Tape

- Determine a procedure to measure how many steps you take in $1$1 minute, and in $3$3 minutes. Make sure you take into account any factors that may affect your data
- Gather any materials you may need to do this. Then perform the experiment.
- Record all of your data in a table
- Find the unit rate for your data.

- Create an equation for how many steps you take per minute using the equation $y=mx+b$
`y`=`m``x`+`b` - Will this equation produce either a vertical or horizontal line? Why or why not?
- What kind of slope will the function have? How do you know?
- In your own words describe what slope is. Interpret this in the context of the problem.
- Graph the function. Put time on the x-axis and the number of steps taken on the y-axis. Be sure to label axes and title the graph.
- What are the $x$
`x`and $y$`y`intercepts of the graph? Does this make sense in the context of the situation? - Work with a partner to answer the rest of the questions.
- Compare your functions. Who walks faster? How do you know?
- Brainstorm some ways to determine how many steps it would take for you to walk across the United States.
- Pick the method you think will be most accurate to estimate the number of steps it takes to walk across the country and compute it.
- How long would it take you to walk across your country? Compare with your partner.

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

Apply algebraic procedures in solving problems