# Go to the Website Desmos. Then, Click on the ‘Math Tools’ Dropdown: Linear and Non-linear Relations Assignment, SWSC, Australia

Subject | Linear and Non-linear Relations |

**Part One: Analyse A Rollercoaster Design**

Note: The rollercoaster is on the next page.

- In which sections of the track is the slope positive? Explain how you know.
- In which sections of the track is the slope negative? Explain how you know.
- Which sections of the graph have the same gradient? (Identity by observing the graph, you don’t need to make any calculations).
- Calculate the gradient for the purple section of the track.
- Calculate the gradient for the red section of the track.
- What is the y-intercept of the graph? What does this value represent?
- How long is the track horizontally?
- How tall is the highest point on the track from the ground?
- Which part of the track do you think would be the scariest? Explain why.

**Part Two: Sketch A Rollercoaster Design**

Q1. Complete the following table of values (show working)

Section 1: = 3 + 1

0

1

2

3

Section 2: = −2 + 18

5

6

7

8

Section 3: = 1

10

11

12

13

Q2. Plot the graphs on the grid paper provided using the co-ordinates from the table of values completed above. Connect the sections of the graph with curved lines.

**Part Three: Finish An Incomplete Design**

- Identify the coordinates of the beginning and endpoints of Section 1.
- Calculate the gradient of the rollercoaster in Section 1.
- By choosing one of the co-ordinates and using the calculated gradient, find the ‘y-intercept’ value of the equation for Section 1.
- Hence, state the equation used to represent Section 1.
- Identify the coordinates of the beginning and endpoints of Section 2.
- Calculate the gradient of the rollercoaster in Section 2.
- By choosing one of the co-ordinates and using the calculated gradient, find the ‘y-intercept’ value of the equation for Section 2.
- Hence, state the equation used to represent Section 2.
- Draw the equations on the graph provided to complete the rollercoaster design.

**Part Four: Create Your Own Design**

Go to the website Desmos (LINK: https://www.desmos.com/). Then, click on the ‘Math Tools’ dropdown and select ‘Graphing Calculator’. This is where you will be able to create your own rollercoaster design.

The rollercoaster design must follow the following guidelines:

- It has at least one section with a positive gradient.
- It has at least one section with a negative gradient.
- It never goes above 20 meters tall.
- It never hits the ground (0 meters).
- It is between 20 metres and 80 metres in horizontal length.
- The slope/gradient is never greater than 5.5 or less than -5.5.
- The track must start and finish horizontally and be at the same height at the beginning and end.

Here are some hints to help you with your design:

- The y-axis represents how far from the ground a particular point is.
- The x-axis represents the horizontal distance of the track.
- Start off each equation by writing ‘y = ‘.
- Use the curly brackets { } to show where you want a section of the graph to start and stop. For example, {0 ≤ 𝑥𝑥 ≤ 5} will draw the graph from 0 to 5 along the x-axis.
- You are NOT expected to find the equations for any curved sections of the track. Instead, focus on creating the straight sections of the track and connect them with curved lines.

Once you have finished your design, you need to write about your design. Make sure to talk about the following:

- Context: How long is your design? How tall is the tallest point of your design? What is the general shape of your design? Why do we need curved sections to connect the lines rather than having straight lines connecting directly?
- Gradients: Where are there positive and negative gradients? What are the values of the gradients in these sections? Which gradients are steeper or less steep?
- Y-intercepts: What is the y-intercept for your graph? What does it represent? What do the y-intercepts in your other equations represent?
- Equations: What were the equations which represented the different sections of your graph? Why did you use those equations in your design?
- Calculations: Give a worked example of how you could have calculated the gradient of one of your lines by hand using two coordinate points. Also, give an example of how you could have found the equation for one of your lines by hand using two coordinate points.

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