1. Created by Mr.Lafferty Maths Dept
Straight Line Graphs
Int 2
Drawing Straight line graphs
The gradient
The gradient from coordinates
The y intercept y = mx + c
Other forms / rearranging equation
31-Mar-17
Created by Mr.Lafferty Maths Dept

2. Created by Mr.Lafferty Maths Dept
Starter Questions
Int 2
Q1. A house is valued at £
Calculate its value after 4 years, if it appreciates by 5% each year.
Q2. Calculate 3.36 x 70 to 2 significant figures.
Q3. Calculate the volume of a cylinder with radius 5cm
and height 100 cm.
31-Mar-17
Created by Mr.Lafferty Maths Dept

3. Created by Mr.Lafferty Maths Dept
Straight Line Graphs
Int 2
Learning Intention
Success Criteria
To draw graphs by using a coordinate table
Understand the key points of drawing a straight line graph
Be able to plot a straight line graph
31-Mar-17
Created by Mr.Lafferty Maths Dept

4. Drawing Straight Line Graphs y = mx + c y = x1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-10 x y x y 3 -4
y = 3x+1 3 -4 x y -2 2 -5 1 7
y = x - 3
y = 2x x y 4 8 x y 3 -4 -3 1 5 6 -8
31-Mar-17
Created by Mr. Lafferty Maths Dept

5. Created by Mr.Lafferty Maths Dept
Straight Line Graphs
Int 2
Key Points
Make a table
Calculate and plot 3 coordinates
3. Draw a line through points
31-Mar-17
Created by Mr.Lafferty Maths Dept

6. Created by Mr.Lafferty Maths Dept
Straight Line Graphs
Int 2
Now try Exercise 1
Odd numbers
MIA (page 33)
31-Mar-17
Created by Mr.Lafferty Maths Dept

7. Created by Mr.Lafferty Maths Dept
Starter Questions
Int 2
Q1. Write this number in full to 1 sig. figs
Q2. Calculate the volume of the triangular prism.
20cm
12cm
8cm
31-Mar-17
Created by Mr.Lafferty Maths Dept

8. The Gradient of a Line www.mathsrevision.com Learning Intention
Success Criteria
To explain how to calculate the gradient using right angled triangles
Gradient is :
change in vertical height divided by
change in horizontal distance
2. Calculate simple gradients.
31-Mar-17
Created by Mr.Lafferty Maths Dept

9. Created by Mr.Lafferty Maths Dept
The Gradient
Difference in
y -coordinates
Int 2
The gradient is the measure of steepness of a line
Change in vertical height
Change in horizontal distance
Difference in
x -coordinates
The steeper a line the bigger the gradient
31-Mar-17
Created by Mr.Lafferty Maths Dept

10. Created by Mr.Lafferty Maths Dept
The Gradient
Int 2 3
m = V = H 4 3
m = V = H 2 3
m = V = H 5 2
m = V = H 6
31-Mar-17
Created by Mr.Lafferty Maths Dept

11. Created by Mr.Lafferty Maths Dept
The Gradient
Int 2
Round the class
Exercise 2
MIA (page 36)
31-Mar-17
Created by Mr.Lafferty Maths Dept

12. Created by Mr.Lafferty Maths Dept
The Gradient of a Line
Int 2
Learning Intention
Success Criteria
To explain positive and negative gradients using coordinates.
Know gradient formula.
2. Calculate gradients given two coordinates.
31-Mar-17
Created by Mr.Lafferty Maths Dept

13. The gradient using coordinates
Mr. Lafferty
The gradient using coordinates
Int 2
m = gradient
y-axis
m = Y2 – Y1
X2 – X1 y2
We start by find the equation of a circle centre the origin.
First draw set axises x,y and then label the origin O.
Next we plot a point P say, which as coordinates x,y.
Next draw a line from the origin O to the point P and label
length of this line r.
If we now rotate the point P through 360 degrees keep the Origin fixed we trace out a circle with radius r and centre O.
Remembering Pythagoras’s Theorem from Standard grade
a square plus b squared equal c squares we can now write down the equal of any circle with centre the origin. y1 O
x-axis x1 x2
31-Mar-17

14. The gradient using coordinates
Mr. Lafferty
The gradient using coordinates
Int 2
Find the gradient of the line.
m = gradient
y-axis
m = Y2 – Y1
X2 – X1
m = 10 – 4
5 – 2
We start by find the equation of a circle centre the origin.
First draw set axises x,y and then label the origin O.
Next we plot a point P say, which as coordinates x,y.
Next draw a line from the origin O to the point P and label
length of this line r.
If we now rotate the point P through 360 degrees keep the Origin fixed we trace out a circle with radius r and centre O.
Remembering Pythagoras’s Theorem from Standard grade
a square plus b squared equal c squares we can now write down the equal of any circle with centre the origin.
m = 6 = 2 3 O
x-axis
31-Mar-17

15. The gradient using coordinates
Mr. Lafferty
The gradient using coordinates
Int 2
Find the gradient of the two lines.
y-axis
m = Y2 – Y1
X2 – X1
m = Y2 – Y1
X2 – X1
m =
3 - 1
m = 8 – 2
-3 – (-1)
We start by find the equation of a circle centre the origin.
First draw set axises x,y and then label the origin O.
Next we plot a point P say, which as coordinates x,y.
Next draw a line from the origin O to the point P and label
length of this line r.
If we now rotate the point P through 360 degrees keep the Origin fixed we trace out a circle with radius r and centre O.
Remembering Pythagoras’s Theorem from Standard grade
a square plus b squared equal c squares we can now write down the equal of any circle with centre the origin.
m = 6 = -3 -2
m = 6 = 3 2 O
x-axis
31-Mar-17

16. The gradient using coordinates
Int 2
The gradient formula is :
Gradient = m =
(y2 – y1)
(x2 – x1)
It is a measure of how steep a line is
A line sloping up from left to right is a positive gradient
A line sloping down from left to right is a negative gradient
31-Mar-17
Created by Mr.Lafferty Maths Dept

17. The gradient using coordinates
Int 2
Exercise 3
Q1 – Q3
MIA (page 37)
31-Mar-17
Created by Mr.Lafferty Maths Dept

18. Created by Mr.Lafferty Maths Dept
Starter Questions
Int 2
Q1. Write out in full to 2 sig. figs.
Q2. A superstore make 20% profit on each can of
soup they sell. If they buy in a can for 50p.
What is the selling price.
Q3. A hemisphere has a diameter of 10cm.
Calculate its volume.
31-Mar-17
Created by Mr.Lafferty Maths Dept

19. Created by Mr.Lafferty Maths Dept
The Gradient of a Line
Int 2
Learning Intention
Success Criteria
To explain the connection between the straight line equation and the gradient.
Understand the term standard form.
2. Identify the gradient m from the standard form.
31-Mar-17
Created by Mr.Lafferty Maths Dept

20. Created by Mr. Lafferty Maths Dept
Straight line equation and the gradient connection 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-10 x y
y = -x - 5
y = 2x + 1 x y 1 3 x y 1 3 -5 -6 -8 1 3 7
m = -1
m = 2
31-Mar-17
Created by Mr. Lafferty Maths Dept

21. Straight Line Equation
S4 Credit
All straight lines have the equation of the form
y = mx + c
Let’s investigate properties
(You need GeoGebra to run link)
31-Mar-17
Created by Mr.Lafferty Maths Dept

22. Straight Line Equationy 10
lines are parallel if they have the same gradient
All straight lines have
the equation of the form 9 8
y = mx + c 7 6 5 4 3
Where line
meets y-axis 2
Gradient 1 x 1 2 3 4 5 6 7 8 9 10
Find the equations of the following lines
y = x
y = x+4
y = 4x+2
y = -0.5x+2
31-Mar-17
Created by Mr.Lafferty Maths Dept

23. Created by Mr.Lafferty Maths Dept
The Gradient of a Line
Int 2
Now try Exercise 3
Q4 – Q9
MIA (page 38)
31-Mar-17
Created by Mr.Lafferty Maths Dept

24. Created by Mr.Lafferty Maths Dept
Starter Questions
Int 2
Q1. Write out in full to 1 significant fig.
Q2. A computer store buys in a laptop for £500.
They want to make a 40% profit.
How much do they sell it for.
Q3. A line is parallel to y = 2x.
Write down its equation
31-Mar-17
Created by Mr.Lafferty Maths Dept

25. Straight Line Equation
lines are parallel if same gradient
Straight Line Equation
All straight lines have the equation of the form
Slope left to right upwards positive gradient
y = mx + c
y - intercept
Gradient
y intercept is were line cuts y axis
Slope left to right downwards negative gradient
31-Mar-17
Created by Mr.Lafferty Maths Dept

26. Created by Mr.Lafferty Maths Dept
Straight Line Graphs
Int 2
Now try Exercise 4
MIA (page 41 )
31-Mar-17
Created by Mr.Lafferty Maths Dept

27. Created by Mr.Lafferty Maths Dept
Starter Questions
Int 2
Q1. The points ( 1, 4) and (3, 11) lie on a line.
Find the gradient of the line.
Q2. Complete the table given : y = 3x+1 x -3 3 y
Q3. Are the two lines parallel. Explain answer
y = x and y = 2x + 2
31-Mar-17
Created by Mr.Lafferty Maths Dept

28. Straight Line Equation
Int 2
Learning Intention
Success Criteria
To show how to rearrange straight line equations into standard form and then identify the gradient and the
y - intercept.
Be able to rearrange straight line equations.
y = mx + c
Identify the gradient m and y – intercept c from the standard form.
y = mx + c
31-Mar-17
Created by Mr.Lafferty Maths Dept

29. Straight Line Equation
This is called the standard form
Straight Line Equation
All straight lines have an equation of the form
y = mx + c
Where line
meets y-axis
Gradient
If two lines have the same gradient they are parallel.
y = 2x
y = 2x+4
31-Mar-17
Created by Mr.Lafferty Maths Dept

30. Straight Line Equation
Just a bit of algebra
Straight Line Equation
Rearrange the following straight line equations into standard form and identify the gradient and y-intercept.
Standard form m c
y – 3x = 4
y = 3x + 4 3 4
2y – 2x = 6
y = x + 3 1 3
y – x + 5 = 0
y = x - 5 1 -5
4y – 8 = 0
y = 2 2
31-Mar-17
Created by Mr.Lafferty Maths Dept

31. Straight Line Equation
Find the a line parallel to y – x = 0 and passing through (0,3).
Standard form m c
x – y = 0
y = x 1
A line parallel to y = x has same gradient therefore m = 1
Since it passes through (0,3) then c = 3
Using standard form line is y = x + 3
31-Mar-17
Created by Mr.Lafferty Maths Dept

32. Straight Line Equation
Int 2
Now try Ex 5
MIA (page 45)
31-Mar-17
Created by Mr.Lafferty Maths Dept