1. Straight Line Graphs Lesson Objectives:
Finding the equation of simple straight line graphs
Looking at relationships between different straight line graphs

2. Every x co-ordinate is the same as every y co-ordinate
We can plot the points: (1 , 1) y x 1 2 3 4 5 6 7 8 -1 -2 -3 -6 -7 -5 -4 -8
(2 , 2) ×
(3 , 3) × ×
What will our next few points will be?
What is the equation of this line? × × ×
We can join these points with a straight line:
y = x
Every x co-ordinate is the same as every y co-ordinate × × ×
We can extend the line through the negative coordinates × × ×
What do you notice about the x and y co-ordinates?

3. y = x x y We can use a table of results help plot the line. -4 -3 -2
We can plot the points: (1 , 1) y x 1 2 3 4 5 6 7 8 -1 -2 -3 -6 -7 -5 -4 -8 ×
(2 , 2)
(3 , 3)
y = x
We can use a table of results help plot the line. x y -4 -3 -2 -1 1 2 3 4 -3 -1 1 2 3 4 -4 -2

4. What two things do you notice?
y = x + 4
y = x + 2 y x 1 2 3 4 5 6 7 8 -1 -2 -3 -6 -7 -5 -4 -8
y = x
y = x - 3
What two things do you notice?
Can you think of another equation?

5. The same rule applies for any value of x eg. 2x
y = 2x + 4
y = 2x y x 1 2 3 4 5 6 7 8 -1 -2 -3 -6 -7 -5 -4 -8
y = 2x - 6
The same rule applies for any value of x eg. 2x

6. You can see that the lines using 3x are all parallel.
y = 3x + 6
y = 3x y x 1 2 3 4 5 6 7 8 -1 -2 -3 -6 -7 -5 -4 -8
y = 3x - 3
You can see that the lines using 3x are all parallel.

7. y = 3x y = 2x y = x y = ½ x y x 8 7 6 5 4 3 2 1 -1 -2 -3 -6 -8 -7 -5-1 -2 -3 -6 -8 -7 -5 -4
y = ½ x

8. What is the equation of the following line?y x 1 2 3 4 5 6 7 8 -1 -2 -3 -6 -7 -5 -4 -8
Hint: It is related to the graph of
y = x

9. What is the equation of the following line?y x 1 2 3 4 5 6 7 8 -1 -2 -3 -6 -7 -5 -4 -8

10. What is the equation of the following line?y x 1 2 3 4 5 6 7 8 -1 -2 -3 -6 -7 -5 -4 -8

11. Let’s end with a difficult one!!!y x 1 2 3 4 5 6 7 8 -1 -2 -3 -6 -7 -5 -4 -8
Can you work out the equation of this line?

12. What key points have you learnt this lesson?