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

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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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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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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

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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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