Straight Line Graphs

1
Straight Line Graphs
S4 Credit
The gradient Vertical Horizontal
The gradient from Coordinates
Drawing Straight line graphs
General Equation y mx c
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Equation from 2 Points
Modelling Situations
Best fitting straight line
Exam Type Questions
2
Starter Questions
S4 Credit
Q1. Calculate 7 5 x 2
Q2. Calculate
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Q3. Is this triangle right angled ? Explain
9
8
5
3
The Gradient of a Line
S4 Credit
Learning Intention
Success Criteria

1. To show how to get the equations for horizontal
   and vertical lines.

1. Understand that vertical lines have equations of
   the form x a

2. Understand that horizontal lines have
equations of the form y a
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4
Equations for Vertical and Horizontal lines
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
5
The Gradient
S4 Credit
Now Try MIA Exercise 2.1 Ch7 (page 136)
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6
Starter Questions
S4 Credit
Q1. Write this number in full to 1 sig. figs
Q2. Calculate the volume of the triangular prism.
20cm
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12cm
8cm
7
The Gradient of a Line
S4 Credit
Learning Intention
Success Criteria

1. To explain how to calculate the gradient using a
   right angle triangle

• Gradient is
• change in vertical height divided by
• change in horizontal distance

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2. Calculate simple gradients.
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The Gradient
Difference in y -coordinates
S4 Credit
The gradient is the measure of steepness of a line
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Difference in x -coordinates
The steeper a line the bigger the gradient
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The Gradient
S4 Credit
3
4
3
2
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3
5
2
6
10
The Gradient
S4 Credit
Now Try MIA Exercise 3.1 Ch7 (page 139)
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Starter Questions
S4 Credit
Q1. A house 4 years ago is valued at 50 000.
Calculate its value if it has increased
by 5.
Q2. Calculate 3.36 x 70 to 2 significant figures.
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Q3. Write down the 3 ways of factorising.
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The Gradient of a Line
S4 Credit
Learning Intention
Success Criteria

1. To explain positive and negative gradients using
   coordinates.

1. Know gradient formula.

2. Calculate gradients given two coordinates.
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13
The gradient using coordinates
S4 Credit
y-axis
y2
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y1
x-axis
O
x1
x2
14
The gradient using coordinates
S4 Credit
Find the gradient of the line.
y-axis
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x-axis
O
15
The gradient using coordinates
S4 Credit
Find the gradient of the two lines.
y-axis
x-axis
O
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The gradient using coordinates
S4 Credit
The gradient formula is
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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
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The gradient using coordinates
S4 Credit
Now try MIA Ex 4.2 Ch7 (page 143)
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Straight Line Graphs
S4 Credit
Learning Intention
Success Criteria

1. To draw graphs by using a coordinate table

1. Understand the keypoints of drawing a straight
   line graph

1. Be able to plot a straight line graph

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Drawing Straight Line Graphs y ax b
y x
x y
0
3
-4
y 3x1
0
3
-4
x y
2
-2
0
-5
1
7
y 2x
y x - 3
x y
x y
0
4
8
0
3
-4
-3
1
5
0
6
-8
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Straight Line Graphs
S4 Credit

• Key Points
• Make a table
• Calculate and plot 3 coordinates
• 3. Draw a line through points

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21
Straight Line Graphs
S4 Credit
Now try MIA Ex5.1 Q5 Only Ch7 (page 145)
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22
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.
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Q3. Explain why 4x2 16 4(x 2)( x 2)
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The Straight Line Equation
S4 Credit
Learning Intention
Success Criteria

1. To explain the connection between the straight
   line equation and the gradient.

1. Understand the term standard form.

2. Identity the gradient m from the standard form.
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Straight line equation and the gradient connection
y -x - 5
y 2x 1
x y
3
0
1
x y
0
1
3
-5
-6
-8
1
3
7
m -1
m 2
25
Straight Line Equation
S4 Credit
All straight lines have the equation of the form
y mx c
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Lets investigate properties
(You need GeoGebra to run link)
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Straight Line Equation
y
S4 Credit
10
All straight lines have the equation of the form
lines are parallel if they have the same gradient
9
8
y mx c
7
6
5
4
3
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Where line meets y-axis
2
Gradient
1
x
0
10
7
4
1
2
3
5
6
8
9
Find the equations of the following lines
y -0.5x2
y x
y x4
y 4x2
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The Gradient of a Line
S4 Credit
Now try MIA Ex 6.1 Ch7 (page 146)
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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.
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Q3. A line is parallel to y 2x. Write down
its equation
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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
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y - intercept
Gradient
y intercept is were line cuts y axis
Slope left to right downwards negative gradient
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Equation of a Straight Line
y mxc
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)

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31
Equation of a Straight Line
y mxc
S4 Credit
Find the equation of the straight line passing
through the points (4, 4) and (8,24).
Solution
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Using the point (4,4) and the gradient m 5 sub
into straight line equation
4 5 x 4 c
c 4 - 20 -16
y mx c
?
?
Equation
y 5x - 16
32
Equation of a Straight Line
y mxc
S4 Credit
Find the equation of the straight line passing
through the points (3, -5) and (6,4).
Solution
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Using the point (6,4) and the gradient m 3 sub
into straight line equation
4 3 x 6 c
c 4 - 18 -14
y mx c
?
?
Equation
y 3x - 14
33
Straight Line Graphs
S4 Credit
Now try MIA Ex 6.2 Ch7 (page 147 )
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34
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 0 3
y
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Q3. Are the two lines parallel. Explain your
answer
y x 2 and y 2x 2
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Modelling Using Straight Line Equation
S4 Credit
Learning Intention
Success Criteria

1. How to model real life situations using straight
   line theory

1. Be able to work out gradient and y intercept
   using a graph.

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1. Form an equation for any straight line graph.

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Pick any 2 points
Modelling Real life
The cost for hiring a plumber per hour is shown
below
10
(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 10x10 30 130
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Pick any 2 points
Modelling Real life
The graph shows how a the volume of water tank
drains over time.
-5
(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
38
Straight Line Equation
S4 Credit
Now try Ex 7.1 MIA (page 149)
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39
Starter Questions
S4 Credit
Q1. The points ( 5, 7) and (7, 21) lie on the
same line. Find the gradient of the line.
Q2. Complete the table given y 2x 10
x -3 0 3
y
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Q3. Are the two lines parallel. Explain answer
y -2x 1 and y 2x 1
40
Best Fit Straight Line Equation
S4 Credit
Learning Intention
Success Criteria

1. How to model real life situations using straight
   line theory

1. Be able to work out gradient and y intercept
   using a graph.

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1. Form an equation for any straight line graph.

41
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

• Draw in the best-fit line and
• find an equation relating
• height and weight.

x
(70,180)
2.57
c 0
0
(0,0)
x
h
w

(d) What height is a pupils who weights 40 kgs?
w 40
h 2.57x40 102.8 cms
42
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
(0,18)

• Draw in the best-fit line and
• find an equation relating
• value and year.

x
(8,8)
x
-1.25
c 18
18
v
y

(d) What is the cost of a car after 4years?
y 4
v -1.25x 4 18 13
Value 13 000
43
Best Fit Straight Line Equation
S4 Credit
Now try Ex 8.1 MIA (page 151)
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44
Exam Type Straight Line Questions

• Example
• The graph shows an electricians charging system.
  
• He has a call-out charge plus an hourly rate.

S4 Credit
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a) Work out the equation of the line. b)
Calculate the cost of a 10 hour job.
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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

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
30
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So the equation is C 10 T 30
C 10 x 10 30 130
b) Find C when T 10
The cost of a 10 hr job is 130.
46
Exam Type Straight Line Questions
S4 Credit
The tank of a car contains 5 litres of petrol.
1.
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.
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Find the equation of the straight line in terms
of V and t.
47
Exam Type Straight Line Questions
S4 Credit
In the diagram below. A is the point (-1, -7)
and B is the point (4, 3).
2.

• (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.

48
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.
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(a) Using the information in the diagram, show
that the equation of the line AB is 3y x 6.
49
Exam Type Straight Line Questions
S4 Credit

• An emergency outlet pipe has to be built across
  the main pipe. The line representing this outlet
  pipe has equation
• 4y 5x 46.

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Calculate the coordinates of the point on the
diagram at which the outlet pipe will cut across
the main water pipe.
50
Exam Type Straight Line Questions
S4 Credit
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