Points of Intersection using Algebra L O All

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

Key Words: Linear Equation Intercept Y intercept Gradient

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

Starter: describe the intersection of two lines using graphs

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

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?

Main: find the intersection of two graphs algebraically Let’s try y=3 x-1 and y=2 x+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?

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

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

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

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

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

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

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

Plenary:

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