Straight Line Graphs

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Straight Line Graphs
Int 2
Drawing Straight line graphs
The gradient
The gradient from coordinates
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The y intercept y mx c
Other forms / rearranging equation
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Starter Questions
Int 2
Q1. A house is valued at 50 000.
Calculate its value after 4 years, if it
appreciates by 5 each year.
Q2. Calculate 3.36 x 70 to 2 significant figures.
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Q3. Calculate the volume of a cylinder with
radius 5cm and height 100 cm.
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Straight Line Graphs
Int 2
Learning Intention
Success Criteria

1. To draw graphs by using a coordinate table

1. Understand the key points of drawing a straight
   line graph

1. Be able to plot a straight line graph

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Drawing Straight Line Graphs y mx c
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
Int 2

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

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Straight Line Graphs
Int 2
Now try Exercise 1 Odd numbers MIA (page 33)
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Starter Questions
Int 2
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
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The Gradient of a Line
Int 2
Learning Intention
Success Criteria

1. To explain how to calculate the gradient using
   right angled triangles

• 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
Int 2
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
Int 2
3
4
3
2
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3
5
2
m V H
6
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The Gradient
Int 2
Round the class Exercise 2 MIA (page 36)
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The Gradient of a Line
Int 2
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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The gradient using coordinates
Int 2
y-axis
y2
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y1
x-axis
O
x1
x2
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The gradient using coordinates
Int 2
Find the gradient of the line.
y-axis
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x-axis
O
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The gradient using coordinates
Int 2
Find the gradient of the two lines.
y-axis
x-axis
O
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The gradient using coordinates
Int 2
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
Int 2
Exercise 3 Q1 Q3 MIA (page 37)
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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.
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Q3. A hemisphere has a diameter of 10cm.
Calculate its volume.
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The Gradient of a Line
Int 2
Learning Intention
Success Criteria

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

1. Understand the term standard form.

2. Identify 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
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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
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
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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
Int 2
Now try Exercise 3 Q4 Q9 MIA (page 38)
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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.
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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
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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Straight Line Graphs
Int 2
Now try Exercise 4 MIA (page 41 )
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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 3x1
x -3 0 3
y
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Q3. Are the two lines parallel. Explain answer
y x 2 and y 2x 2
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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

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• Identify the gradient m and y intercept c from
  the standard form.
• y mx c

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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
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If two lines have the same gradient they are
parallel.
y 2x
y 2x4
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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
c
m
y 3x 4
y 3x 4
3
4
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2y 2x 6
y x 3
1
3
y x 5 0
y x - 5
1
-5
4y 8 0
y 2
0
2
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Straight Line Equation
Find the a line parallel to y x 0 and passing
through (0,3).
Standard form
c
m
x y 0
y x
1
0
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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
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Straight Line Equation
Int 2
Now try Ex 5 MIA (page 45)
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