1. Linear
Geometry

2. You have already completed the bridging booklet
Reminder
You have already completed the bridging booklet
chapter 9 Linear graphs
If you need support with any of the following you MUST see your teacher
Rearranging a linear equation to find the gradient and intercept
Drawing a line from an equation

3. Starter: Ten questions
Linear coord geometry
KUS objectives
BAT explore gradients of parallel and perpendicular line
BAT rearrange and find equations of lines
Starter: Ten questions
Identify the equation of each of the following line graphs

4. Starter: identify linear equationsx
Starter: identify linear equations
Identify the equations
of these lines

5. Answers y = 2x + 3 y = 2x - 4 y = 3x + 1 y = -2x + 5 y = x + 2 y = 3

6. Notes: General equation of a line
We are used to:
gradient
y-intercept
Another ‘standard way to write the equation of
a line is:
The General form of the equation of a line

7. For each of these equations, i) rearrange it into the form y = mx + c
WB1
gradient and y intercept
For each of these equations,
i) rearrange it into the form y = mx + c
ii) give the gradient
iii) give the intercept on the y-axis. 10
Gradient m = -2
Gradient m = 2.5 3
Intercept (0, 10)
Intercept (0, 3)

8. y y = 3 x x y = 3 x + 1 y = 3 x + 2 y = 3 x + 3 y = 3 x + 4
Notes 1
y = 3 x
y = 3 x + 1
y = 3 x + 2
y = 3 x + 3
y = 3 x + 4
y = 3 x + 5
y = 3 x – 1
y = 3 x – 2 x
y = 3 x – 3
y = 3 x – 4
The ‘family’ of Parallel lines with equation
y = 3x + a

9. There are three sets of parallel lines here.
Challenge 1
There are three sets of parallel lines here.
Match them up and say what the gradient is for each set.

10. General equation intersection points
Why bother with the general equation?
Solve these simultaneous equations:
Easier to work with:

11. General equation intersection points
Why bother with the general equation?
Solve these
simultaneous equations:
The solution is the Intersection point of the two lines
(-2, -½)

12. Which of these lines are parallel to the line 3x - 2y – 4 = 0
Challenge 2
Which of these lines are parallel to the line 3x - 2y – 4 = 0

13. These lines are perpendicular
Notes
These lines are perpendicular
Define perpendicular = at right angles

14. Notes
What is each gradient? 1 2
Gradient = ½ 2
Gradient = -2 1

15. Notes
What is each gradient?
Gradient = 3 1 3 3 1
Gradient = -1/3

16. PERPENDICULAR LINE IS THE
Notes 1
THE GRADIENT OF A
PERPENDICULAR LINE IS THE
NEGATIVE RECIPROCAL
OF THE OTHER
𝒎 𝟏 × 𝒎 𝟐 =−𝟏

17. y x What do you notice? Draw a Perpendicular line to y = 3x
Notes
Draw a Perpendicular line
to y = 3x
What do you notice?
The ‘family’ of Perpendicular lines with general equation
y = -1/3x + a

18. gradient y-intercept 2 -5 Examples: We are used to:
Notes
We are used to:
gradient
y-intercept
The Perpendicular line has
gradient m2 where:
line
perpendicular 2 -5
Examples:

19. What is the gradient of the lines perpendicular to these?
Practice 1
What is the gradient of the lines perpendicular to these?
y = 2x + 1
m = 2
-1/m= -1/2
y = 2 + 4x
m = 4
-1/m= -1/4
y = 3x + 2
m = 3
-1/m= -1/3
y + 2x = 2
m = -2
-1/m= 1/2
2y = 3x - 2
m = 3/2
-1/m= -2/3
5y + 2x = 3
m = -2/5
-1/m= 5/2

20. WB2
Give the General equation of the perpendicular line to 2𝑥+𝑦−8=0 that goes through (4, 9)
Has gradient m1 = -2
So the gradient of a perpendicular line is
m2 = ½
When x = 4, y = 9 … so

21. WB3
Give the General equation of the perpendicular line to 𝑥+5𝑦−6=0 that goes through ( 3 5 , 7)
Has gradient m1 = -1/5
So the gradient of a perpendicular line is
m2 = 5
When x = 3/5, y = 7 … so

22. First the midpoint of line AB is (−1. 4)
WB4
Two points A(1,2) and B(-3,6) are joined to make the line AB.
Find the equation of the perpendicular bisector of AB
First the midpoint of line AB is
(−1. 4)
𝑚 1 = 6−2 −3−1 =−1
2nd the gradient of line AB is
So the perpendicular gradient is
𝑚 2 =1
𝑦=𝑥+ ?
When x =1, y = 2 so
𝑦=𝑥+1
Is the perpendicular bisector of line AB

23. BAT rearrange and find equations of lines
KUS objectives BAT explore gradients of parallel and perpendicular line
BAT rearrange and find equations of lines
self-assess
One thing learned is –
One thing to improve is –

24. END