1. Points of Intersection using Algebra
L.O.
All pupils can describe the intersection of two lines using graphs
All pupils can describe how to find the intersection of two graphs algebraically
Some pupils can find the intersection of two graphs when rearranging is required

2. Key Words:
Linear
Equation
Intercept
Y intercept
Gradient

3. Points of Intersection using Algebra
L.O.
All pupils can describe the intersection of two lines using graphs
All pupils can describe how to find the intersection of two graphs algebraically
Some pupils can find the intersection of two graphs when rearranging is required

4. describe the intersection of two lines using graphs
Starter:
describe the intersection of two lines using graphs

5. Points of Intersection using Algebra
L.O.
All pupils can describe the intersection of two lines using graphs
All pupils can describe how to find the intersection of two graphs algebraically
Some pupils can find the intersection of two graphs when rearranging is required

6. find the intersection of two graphs algebraically
Main:
find the intersection of two graphs algebraically
Any ideas as to how we can find the point where the x and y values are the same on the two graphs?

7. At the point where they meet, the coordinates are the same.
Main:
find the intersection of two graphs algebraically
Let’s try
y=3x-1 and y=2x+2
At the point where they meet, the coordinates are the same.
So do you agree that the two equations must have the same y values?

8. And, if they have the same y values we can write:
Main:
find the intersection of two graphs algebraically
y=3x-1 and y=2x+2
We can write:
3x-1=y and y=2x+2
And, if they have the same y values we can write:
3x-1=y=y=2x+2
3x-1=2x+2

9. find the intersection of two graphs algebraically
Main:
find the intersection of two graphs algebraically
y=3x-1 and y=2x+2
3x-1=2x+2
Can you solve this for x?
3x-2x=2+1
x=3
So our x coordinate is 3!

10. If x=3, how can we find the y coordinate?
Main:
find the intersection of two graphs algebraically
y=3x-1 and y=2x+2
If x=3, how can we find the y coordinate?
y=3x-1
By substitution of x=3:
y=3x3-1
y=9-1
y=8

11. So the point of intersection between y=3x-1 and y=2x+2
Main:
find the intersection of two graphs algebraically
So the point of intersection between y=3x-1 and y=2x+2 is
(3,8)

12. SIMULTANEOUS EQUATIONS! Another example on the board…
Main:
find the intersection of two graphs algebraically
SIMULTANEOUS EQUATIONS!
Another example on the board…

13. Main: find the gradient and intercept of graphs
find the intersection of two graphs when rearranging is required

14. Points of Intersection using Algebra
L.O.
All pupils can describe the intersection of two lines using graphs
All pupils can describe how to find the intersection of two graphs algebraically
Some pupils can find the intersection of two graphs when rearranging is required

15. Plenary:

16. Points of Intersection using Algebra
L.O.
All pupils can describe the intersection of two lines using graphs
All pupils can describe how to find the intersection of two graphs algebraically
Some pupils can find the intersection of two graphs when rearranging is required