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

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?

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

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?

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

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.

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

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

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

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

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?

What key points have you learnt this lesson?