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Drawing Linear GraphsThe cover up method
The Cover up method (the x-axis)
The Cover up method (the y-axis)
Using the facts
Using Cover up
Your turn – Question 1
Your turn – Question 2
Your turn – Question 3
Your turn – Question 4
Examples panel
www.mandymaths.co.uk
The x-axis
The x-axis has the equation y = 0because all points on the x-axis have a y value of 0
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x xx x x(-2,0) (2.5,0
)(-4,0) (0,0) (5,0)
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The y-axis
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The y-axis has the equation x = 0because all points on the y-axis have an x value of 0
(0,4)
(0,2)
(0,0)
(0,-1.5)
(0,-4)
x
x
x
x
x
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Using the facts
We can use the fact that• The x-axis has the equation y = 0• The y-axis has the equation x = 0to draw any line with the equation ax + by = c
Example – Draw the graph of 2x + y = 4
Substituting x = 0 into the equation we can solve for y2(0) + y = 4 y = 4
The line passes through the point (0,4) on the y-axis
Substituting y = 0 into the equation we can solve for x
2x + 0 = 4
2x = 4 x = 2
The line passes through the point (2,0) on the x-axis
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x
x
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Using cover up
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This type of equation can be drawn easily using the cover up method1. Write down the equation
2. Cover up the x term
3. Solve the equation y = 4
4. Cover up the y term
5. Solve the equation 2x = 4 x = 2
6. This gives us the points 4 on the y-axis and 2 on the x-axis
x
x
2x + y = 4
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Question 1
Draw the following lines using the cover up method.
You can use the same grid taking both x and y axes from -10 to +10
a) 3x - y = 6
b) 2x - 3y = 12
c) y + 3x = 9
d) 3x + 2y – 18 = 0
e) 2x + y + 10 = 2
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Question 2 Main panel
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Draw the following lines using the cover up method.
You can use the same grid taking both x and y axes from -5 to +5
a) y + x = 5
b) y – x = 2
Write down the coordinates of the point where the two lines cross?
Question 3
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1
56
8
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Solve the simultaneous equations using the cover up method.
Take both x and y axes from -5 to +5
a) y + x = 1
y = x + 2
b) y + x = 5
y – 2 = - x
Question 4
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1
567
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Find the solution of each of the following pairs of simultaneous equations by drawing their graphs.
x - y = 3
4y + x = 8
y = 3 + 2x
5x + y – 10 = 0
y = - x
y – 4x = 5
1 2 3
4 5 6
7 8
Drawing Linear graphsCover up method examples Main panel
x + y = 4
x + y = 4 2
3 4
5 6
7 8
x
x
y = 4 x = 4
Main panel Examples panel
1 x - y = 4
3 4
5 6
7 8x - y = 4
x
x
-y = 4 x = 4
y = -4Main panel Examples panel
1 23x + 2y = 6 4
5 6
7 83x + 2y = 6
x
x
2y = 6 3x = 6
y = 3 x = 2Main panel Examples panel
1 2
3 2x - y = 2
5 6
7 82x - y = 2
x
x
-y = 2 2x = 2
y = -2 x = 1Main panel Examples panel
1 2
33y = 6 – 2x
4
6
7 83y = 6 – 2x
x
x
3y = 6 2x = 6
y = 2 x = 33y + 2x = 6Main panel Examples panel
1 2
3x = y - 4
4
5
7 8x = y - 4
x
x
-y = -4 x = -4
y = 4x - y = - 4Main panel Examples panel
1 2
3
7
4
5 6
86x + 10y – 30 = 0
x
x
10y = 306x = 30
y = 36x + 10y = 30
x = 5Main panel Examples panel
1 2
3
8
4
5 6
7y = 2x + 4
x
x
-2x = 4 y = 4
x = -2y - 2x = 4
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