1. Straight Line Graphs www.mathsrevision.com
S4 Credit
The gradient Vertical ÷ Horizontal
The gradient from Coordinates
Drawing Straight line graphs
General Equation y = mx + c
Equation from 2 Points
Modelling Situations
Best – fitting straight line
Exam Type Questions

2. Created by Mr.Lafferty Maths Dept
Starter Questions
S4 Credit
Q1. Calculate 7 – 5 x 2
Q2. Calculate
Q3. Is this triangle right angled ?
Explain 9 8 5
15-Dec-17
Created by Mr.Lafferty Maths Dept

3. Created by Mr.Lafferty Maths Dept
The Gradient of a Line
S4 Credit
Learning Intention
Success Criteria
To show how to get the equations for horizontal and vertical lines.
Understand that vertical lines have equations of the form x = a
2. Understand that horizontal lines have equations of the form y = a
15-Dec-17
Created by Mr.Lafferty Maths Dept

4. x = -6 Mark the points on your grid below and then join them together
Equations for Vertical and Horizontal lines 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-10 x y
x = -6
Mark the points
on your grid below
and then join them
together
Vertical lines
have equations
of the form
x = 8
Horizontal lines
have equations
of the form
y = 2
y = -9
15-Dec-17
Created by Mr. Lafferty Maths Dept

5. Created by Mr.Lafferty Maths Dept
The Gradient
S4 Credit
Now Try MIA
Exercise 2.1
Ch7 (page 136)
15-Dec-17
Created by Mr.Lafferty Maths Dept

6. Created by Mr.Lafferty Maths Dept
Starter Questions
S4 Credit
Q1. Write this number in full to 1 sig. figs
Q2. Calculate the volume of the triangular prism.
20cm
12cm
8cm
15-Dec-17
Created by Mr.Lafferty Maths Dept

7. The Gradient of a Line www.mathsrevision.com Learning Intention
S4 Credit
Learning Intention
Success Criteria
To explain how to calculate the gradient using a right angle triangle
Gradient is :
change in vertical height divided by
change in horizontal distance
2. Calculate simple gradients.
15-Dec-17
Created by Mr.Lafferty Maths Dept

8. Created by Mr.Lafferty Maths Dept
The Gradient
Difference in
y -coordinates
S4 Credit
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
15-Dec-17
Created by Mr.Lafferty Maths Dept

9. Created by Mr.Lafferty Maths Dept
The Gradient
S4 Credit 3 4 3 2 3 5 2 6
15-Dec-17
Created by Mr.Lafferty Maths Dept

10. Created by Mr.Lafferty Maths Dept
The Gradient
S4 Credit
Now Try MIA
Exercise 3.1
Ch7 (page 139)
15-Dec-17
Created by Mr.Lafferty Maths Dept

11. Created by Mr.Lafferty Maths Dept
Starter Questions
S4 Credit
Q1. A house is valued at £
Calculate it’s 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.
15-Dec-17
Created by Mr.Lafferty Maths Dept

12. Created by Mr.Lafferty Maths Dept
The Gradient of a Line
S4 Credit
Learning Intention
Success Criteria
To explain positive and negative gradients using coordinates.
Know gradient formula.
2. Calculate gradients given two coordinates.
15-Dec-17
Created by Mr.Lafferty Maths Dept

13. The gradient using coordinates
Mr. Lafferty
The gradient using coordinates
S4 Credit
m = gradient
y-axis 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
15-Dec-17

14. The gradient using coordinates
Mr. Lafferty
The gradient using coordinates
S4 Credit
Find the gradient of the line.
m = gradient
y-axis
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. O
x-axis
15-Dec-17

15. The gradient using coordinates
Mr. Lafferty
The gradient using coordinates
S4 Credit
Find the gradient of the two lines.
y-axis
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. O
x-axis
15-Dec-17

16. The gradient using coordinates
S4 Credit
The gradient formula is :
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
15-Dec-17
Created by Mr.Lafferty Maths Dept

17. The gradient using coordinates
S4 Credit
Now try MIA
Ex 4.2
Ch7 (page 143)
15-Dec-17
Created by Mr.Lafferty Maths Dept

18. Created by Mr.Lafferty Maths Dept
Straight Line Graphs
S4 Credit
Learning Intention
Success Criteria
To draw graphs by using a coordinate table
Understand the keypoints of drawing a straight line graph
Be able to plot a straight line graph
15-Dec-17
Created by Mr.Lafferty Maths Dept

19. Drawing Straight Line Graphs y = ax + b 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
15-Dec-17
Created by Mr. Lafferty Maths Dept

20. Created by Mr.Lafferty Maths Dept
Straight Line Graphs
S4 Credit
Key Points
Make a table
Calculate and plot 3 coordinates
3. Draw a line through points
15-Dec-17
Created by Mr.Lafferty Maths Dept

21. Created by Mr.Lafferty Maths Dept
Straight Line Graphs
S4 Credit
Now try MIA
Ex5.1 Q5 Only
Ch7 (page 145)
15-Dec-17
Created by Mr.Lafferty Maths Dept

22. Created by Mr.Lafferty Maths Dept
Starter Questions
S4 Credit
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.
15-Dec-17
Created by Mr.Lafferty Maths Dept

23. The Straight Line Equation
S4 Credit
Learning Intention
Success Criteria
To explain the connection between the straight line equation and the gradient.
Understand the term standard form.
2. Identity the gradient m from the standard form.
15-Dec-17
Created by Mr.Lafferty Maths Dept

24. 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 = 2x - 5
y = 2x + 1 x y 1 3 x y 1 3 -5 -3 1 1 3 7
m = 2
m = 2
15-Dec-17
Created by Mr. Lafferty Maths Dept

25. Straight Line Equation
S4 Credit y 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
15-Dec-17
Created by Mr.Lafferty Maths Dept

26. Created by Mr.Lafferty Maths Dept
The Gradient of a Line
S4 Credit
Now try MIA
Ex 6.1
Ch7 (page 146)
15-Dec-17
Created by Mr.Lafferty Maths Dept

27. Created by Mr.Lafferty Maths Dept
Starter Questions
S4 Credit
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
15-Dec-17
Created by Mr.Lafferty Maths Dept

28. Straight Line Equation
lines are parallel if same gradient
Straight Line Equation
S4 Credit
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
15-Dec-17
Created by Mr.Lafferty Maths Dept

29. Equation of a Straight Line
y = mx+c
S4 Credit
To find the equation of a straight line we need to know
Two points that lie on the line
( x1, y1) and ( x2, y2) Or
The gradient and a point on the line
m and (a,b)
15-Dec-17

30. Equation of a Straight Line
Mr. Lafferty
Equation of a Straight Line
y = mx+c
S4 Credit
Find the equation of the straight line passing through the points (4, 4) and (8,24).
Solution
Using the point (4,4) and the gradient m = 5
sub into straight line equation
We are now in a position to find the equation of any circle with centre A,B.
All we have to do is repeat the process in shown in slide 2, but this time the centre is chosen to be (a,b).
First plot a point C and label it’s coordinates (a,b), next we plot another point P and label it’s coordinates (x,y).
Next draw a line from C to P and call this length (r).
(r) will be the radius of our circle with centre (a,b).
Again we rotate the point P through 360 degrees keeping the point C fixed.
Using Pythagoras Theorem a squared plus b squared equal c squared we can write down the equation of any circle with centre (a,b) and radius (r).
The equation is (x - a) all squared plus (y-b) all squared equals (r) squared.
Finally to write down the equation of a circle we need to know the co-ordinates of the centre and the length of the radius or co-ordinates of the centre and the co-ordinates of a point on the circumference of the circle.
y = mx + c 
4 = 5 x 4 + c 
c = = -16
Equation :
y = 5x - 16

31. Equation of a Straight Line
Mr. Lafferty
Equation of a Straight Line
y = mx+c
S4 Credit
Find the equation of the straight line passing through the points (3, -5) and (6,4).
Solution
Using the point (6,4) and the gradient m = 3
sub into straight line equation
We are now in a position to find the equation of any circle with centre A,B.
All we have to do is repeat the process in shown in slide 2, but this time the centre is chosen to be (a,b).
First plot a point C and label it’s coordinates (a,b), next we plot another point P and label it’s coordinates (x,y).
Next draw a line from C to P and call this length (r).
(r) will be the radius of our circle with centre (a,b).
Again we rotate the point P through 360 degrees keeping the point C fixed.
Using Pythagoras Theorem a squared plus b squared equal c squared we can write down the equation of any circle with centre (a,b) and radius (r).
The equation is (x - a) all squared plus (y-b) all squared equals (r) squared.
Finally to write down the equation of a circle we need to know the co-ordinates of the centre and the length of the radius or co-ordinates of the centre and the co-ordinates of a point on the circumference of the circle.
y = mx + c 
4 = 3 x 6 + c 
c = = -14
Equation :
y = 3x - 14

32. Created by Mr.Lafferty Maths Dept
Straight Line Graphs
S4 Credit
Now try MIA
Ex 6.2
Ch7 (page 147 )
15-Dec-17
Created by Mr.Lafferty Maths Dept

33. Created by Mr.Lafferty Maths Dept
Starter Questions
S4 Credit
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
15-Dec-17
Created by Mr.Lafferty Maths Dept

34. Modelling Using Straight Line Equation
S4 Credit
Learning Intention
Success Criteria
How to model real life situations using straight line theory
Be able to work out gradient and y intercept using a graph.
Form an equation for any straight line graph.
15-Dec-17
Created by Mr.Lafferty Maths Dept

35. The cost for hiring a plumber per hour is shown below
Pick any 2 points
Modelling Real – life
The cost for hiring a plumber per hour is shown below 10 1 2 3 4 5 6 7 8 9 10 T C 20 30 40 50 60 70 80 90
100
Cost £
Time (hours)
(7,100)
(a) Calculate the gradient.
What is the value of C
when T = 0 30 30
Write down an equation
connecting C and T.
(0,30)
C = T +
(d) Find the cost for a plumber for 10 hours?
T = 10
C = 10x = £130

36. (a) Calculate the gradient. (0,80) What is the value of V when T = 0
Pick any 2 points
Modelling Real – life
The graph shows how a the volume of water tank drains over time. -5 1 2 3 4 5 6 7 8 9 10 T V 20 30 40 50 60 70 80 90
100
Volume
Time (mins)
(a) Calculate the gradient.
(0,80)
What is the value of V
when T = 0 80 80
(8,40)
Write down an equation
connecting V and T.
V = T +
(d) How long before the tank is empty?
V = 0
0 = -5xT + 80
T = (-80) ÷(–5) = 16mins

37. Straight Line Equation
S4 Credit
Now try Ex 7.1
MIA (page 149)
15-Dec-17
Created by Mr.Lafferty Maths Dept

38. Created by Mr.Lafferty Maths Dept
Starter Questions
S4 Credit
Q1. The points ( 5, 7) and (7, 21) lie on a line.
Find the gradient of the line.
Q2. Complete the table given : y = 2x + 10 x -3 3 y
Q3. Are the two lines parallel. Explain answer
y = -2x and y = 2x + 1
15-Dec-17
Created by Mr.Lafferty Maths Dept

39. Best Fit Straight Line Equation
S4 Credit
Learning Intention
Success Criteria
How to model real life situations using straight line theory
Be able to work out gradient and y intercept using a graph.
Form an equation for any straight line graph.
15-Dec-17
Created by Mr.Lafferty Maths Dept

40. Best-Fitting Straight line
Data was collected on pupils weight and height. Data is plotted below.
Pick any 2 points
(a) Is there correlation between height and weight.
Yes, a positive correlation 10 20 30 40 50 60 70 80 90
100 w h
120
140
160
180
200
Height (cms)
Weight (Kgs)
Draw in the best-fit line and
find an equation relating
height and weight. x
(70,180)
2.57
c = 0
(0,0) x
h = w +
(d) What height is a pupils who weights 40 kgs?
w = 40
h = 2.57x40 = cms

41. Best-Fitting Straight line
A survey was carried out on the value of cars depending on their age
The data is plotted below.
Pick any 2 points
(a) Is there correlation between value and age.
Yes, a negative correlation 1 2 3 4 5 6 7 8 9 10 y v 12 14 16 18 20
value £ ‘ 000
Years
Draw in the best-fit line and
find an equation relating
value and year.
(0,18) x x
(8,8)
-1.25
c = 18 18
v = y +
(d) What is the cost of a car after 4years?
y = 4
v = -1.25x = 13
Value = £13 000

42. Best Fit Straight Line Equation
S4 Credit
Now try Ex 8.1
MIA (page 151)
15-Dec-17
Created by Mr.Lafferty Maths Dept

43. Straight Line Questions
Exam Type
Straight Line Questions
Example
The graph shows an electrician’s charging system.
He has a call-out charge plus an hourly rate.
S4 Credit
a) Work out the equation of the line.
b) Calculate the cost of a 10 hour job.

44. Straight Line Questions
Exam Type
Straight Line Questions
S4 Credit
a) Pick two convenient points on the line, say (0, 30) and (5, 80).
Thinking of the form y = mx + c
The y-intercept gives c = 30
= 10
The equation is: y = 10x + 30
The label on the y-axis is C and the label on the x-axis is T So the equation is C = 10 T
So the equation is C = 10 T
b) Find C when T = 10
C = 10 x = 130
The cost of a 10 hr job is £130.

45. Straight Line Questions
Exam Type
Straight Line Questions
S4 Credit 1.
The tank of a car contains 5 litres of petrol.
The graph below shows how the volume of petrol in this tank changes as a further 45 litres of petrol is pumped in at a steady rate for 60 seconds.
Find the equation of the straight line in terms of V and t.

46. Straight Line Questions
Exam Type
Straight Line Questions
S4 Credit 2.
In the diagram below.
A is the point (-1, -7) and B is the point (4, 3).
(a) Find the gradient of the line AB.
AB cuts the y-axis at the point (0, -5).
Write down the equation of the line AB.
The point (3k, k) lies on the line AB.
Find the value of k.

47. Straight Line Questions
Exam Type
Straight Line Questions
S4 Credit 3.
A water pipe runs between two buildings. These are represented by the points A and B in the diagram below.
(a) Using the information in the diagram, show that the equation of the line AB is 3y – x = 6.

48. Straight Line Questions
Exam Type
Straight Line Questions
S4 Credit
(b) An emergency outlet pipe has to be built across the main pipe. The line representing this outlet pipe has equation
4y + 5x = 46.
Calculate the coordinates of the point on the diagram at which the outlet pipe will cut across the main water pipe.

49. Straight Line Questions
Exam Type
Straight Line Questions
S4 Credit