What's My Line

Introduction

In today's lesson, you will be plotting different points and finding relationships between them.  You are encouraged to use an online graphing calculator such as Desmos or Geogebra.

You may wish to use these two worksheets: 1 and 2 (PRINT ME) for today's lesson.

Part 1

1. Plot the points on the right on Desmos or Geogebra.  

2. For each question, what is the relationship between the x and y coordinates?  What is the most simple way you can think of to describe the relationship?

Part 2

1. Build some equations in the forms highlighted on the right:

2. What is the same about all of the lines?

3. What happens if the sign is a ‘+’?

4. What happens if the sign is a ‘-’?

5. What happens if the answer is wrong?

6. Does it make a difference if the answer is too high or too low?

7. What other interesting things do you notice?

8. Write down 5 different equations of straight lines which pass through A(3, 5).

9. Write down 5 different equations of straight lines which pass through B(5, 8).

10. Is there any equations in Question 8 same as Question 9?

11. If your answer to Question 10 is no, find the equation of a straight line which passes through both A and B.

Part 3

1. Now, what if you have two points, say (2, 5) and (4, 10), can you think of an equation of the line that goes through both points?

2. Try fitting equations for the points on the right.

3. What is the connection between the coordinate points and the equation of the line that goes through both points?

4. Is there only one equation that goes through both points?  If not, then find other equations.

5. What do you notice about all these equations?

Part 4

1. Create six pairs of points where:

   • Three pairs will produce a line which slopes upwards. 

   • While the other 3 pairs will produce a line which slopes downwards.

2. Complete the second and third columns of the table below using your points in Question 1.

3. Give your table to someone else to work out the equation of straight line in each case.

4. Check that each straight line goes through the two points using Desmos or Geogebra.  

5. Create a poster which gives instructions on how to find the equation of a straight line that goes through two given points in one of forms on the right:

• Give an example on each type of straight lines.

• You should also talk about how each type of equations is related to the appearance of the lines on a graph. 

Further Questions and Challenges

1. How do you determine whether a chosen point is on the line? Above the line? Below the line?

2. Can you rearrange your equations in the form on the right?

   • What have you noticed about the value before x.  What does it determine? 

   • What have you noticed about the value after x.  What does it determine?

Extension

In this lesson, you have been looking at linear relationships.  For the extension, here are some non-linear ones.  In each of the questions on the right:

1. Plot the points on Desmos or Geogebra.  

2. Find a relationship between x and y.

3. Graph your relationship verify that your rule works i.e. the line should go through the points.