This document discusses straight line graphs and various methods for plotting straight lines on a graph. It covers identifying horizontal, vertical and diagonal lines, writing equations in y=mx+c form, using a table method to plot lines by substituting x-values, and using the x=0, y=0 method to find two points and plot a line from its equation. Exercises are provided for students to practice identifying and plotting different types of straight lines.

1. Straight Line Graphs

2. Straight Line Graphs
Sections
1) Horizontal, Vertical and Diagonal Lines
(Exercises)
2) y = mx + c
(Exercises : Naming a Straight Line
Sketching a Straight Line)
3) Plotting a Straight Line - Table Method
(Exercises)
4) Plotting a Straight Line – X = 0, Y = 0 Method
(Exercises)
5) Supporting Exercises
Co-ordinates Negative Numbers Substitution

3. x
y
1
-5
-4
-3
-2
-1
4
3
2
1
-5 -4 -3 -2 0 2 3 54-1
Naming horizontal and vertical lines
(-4,-2) (0,-2) (-4,-2)
y = -2
(3,4)
(3,1)
(3,-5)
x = 3
(x,y)
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4. 1
-5
-4
-3
-2
-1
4
3
2
1
-5 -4 -3 -2 0 2 3 54-1
Now try these lines
(-4,2) (0,2) (-4,2)
y = 2
(-2,4)
(-2,1)
(-2,-5)
x = -2
(x,y)
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y
x

5. -5
-4
-3
-2
-1
4
3
2
1
1-5 -4 -3 -2 0 2 3 54-1
See if you can name lines 1 to 5(x,y)
1
5 3
4
2 Back to Main Page
y
x
y = 1
x = 1 x = 5
y = -4
x = -4

6. 1
-5
-4
-3
-2
-1
4
3
2
1
-5 -4 -3 -2 0 2 3 54-1
Diagonal Lines
(-4,-3) (0,1) (2,3)
(3,3)
(1,1)
(-3,-3)
y = -x
(x,y)
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(2,-2)
(-1,1)
(-3,3)
y = x
y = x + 1
y
x

7. Back to Main Page
1
2
1
-5
-4
-3
-2
-1
4
3
2
1
-5 -4 -3 -2 0 2 3 54-1
3
4
Now see if you can identify these diagonal lines
x
y
y = x - 1
y = x + 1
y = - x - 2
y = -x + 2

8. y = mx + c
Every straight line can be written in this form. To do this the
values for m and c must be found.
y = mx + c
c is known as the intercept
m is known as the gradient
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9. y
x1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
8
–
7 –
6 –
5 –
4 –
3 –
2 –
1 -
1
-
2
-
3
-
4
-
5
-
6
Find the Value of c
This is the point at
which the line crosses
the y-axis.
Find the Value of m
The gradient means
the rate at which the
line is climbing.
Each time the lines
moves 1 place to the
right, it climbs up by 2
places.
Finding m and c
y = 2x +3y = mx +c
So c = 3
So m = 2
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10. y
x1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
8
–
7 –
6 –
5 –
4 –
3 –
2 –
1 -
1
-
2
-
3
-
4
-
5
-
6
Find the Value of c
This is the point at
which the line crosses
the y-axis.
Find the Value of m
The gradient means
the rate at which the
line is climbing.
Each time the line
moves 1 place to the
right, it moves down
by 1 place.
Finding m and c
y = 2x +3y = mx +c
So c = 2
So m = -1
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11. y
x1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
8
–
7 –
6 –
5 –
4 –
3 –
2 –
1 -
1
-
2
-
3
-
4
-
5
-
6
Line 1
m =
c =
Equation:
Some Lines to Identify
Line 2
m =
c =
Equation:
1
2
y = x + 2
Line 3
m =
c =
Equation:
1
-1
y = x - 1
-2
1
y = -2x + 1
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12. y
x1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
8
–
7 –
6 –
5 –
4 –
3 –
2 –
1 -
1
-
2
-
3
-
4
-
5
-
6
Exercise
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Click for Answers
1
2
3
5
4
1) y = x - 2
2) y = -x + 3
3) y = 2x + 2
4) y = -2x - 1
5) y = -2x - 1
2

13. Further Exercise
Sketch the following graphs by using y=mx + c
1) y = x + 4
2) y = x - 2
3) y = 2x + 1
4) y = 2x – 3
5) y = 3x – 2
6) y = 1 – x
7) y = 3 – 2x
8) y = 3x
9) y = x + 2
2
10) y = - x + 1
2
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14. The Table Method
We can use an equation of a line to plot a graph by
substituting values of x into it.
Example
y = 2x + 1
x = 0 y = 2(0) +1 y = 1
x = 1 y = 2(1) +1 y = 3
x = 2 y = 2(2) +1 y = 5
Now you just have to plot the points on to a graph!
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x 0 1 2
y 1 3 5

15. The Table Method
0 1-1 432-2-3-4
-1
-2
-3
-4
1
2
3
4
y = 2x + 1
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x 0 1 2
y 1 3 5

16. The Table Method
Use the table method to plot the following lines:
1) y = x + 3
2) y = 2x – 3
3) y = 2 – x
4) y = 3 – 2x
Click to reveal plotted lines
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x 0 1 2
y

17. The Table Method
0 1-1 432-2-3-4
-1
-2
-3
-4
1
2
3
4
4
3
1
2 Back to Main Page
Click for further
exercises

18. Further Exercise
Using the table method, plot the following graphs.
1) y = x + 2
2) y = x – 3
3) y = 2x + 4
4) y = 2x – 3
5) y = 3x + 1
6) y = 3x – 2
7) y = 1 – x
8) y = 1 – 2x
9) y = 2 – 3x
10) y = x + 1
2
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2

19. This method is used when x and y are on the same side.
Example: x + 2y = 4
The x = 0, y = 0 Method
To draw a straight line we only need 2 points to join
together.
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20. These points are where x = 0 (anywhere along the y
axis) and y = 0 (anywhere along the x axis).
If we find the 2 points where the graph cuts the
axes then we can plot the line.
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21. y
x1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
8
-6 -5 -4 -3 -2 -1-
1
-
2
-
3
-
4
-
5
-
6
This is where the graph
cuts the y – axis (x=0)
This is where the graph
cuts the x – axis (y=0)
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22. By substituting these values into the equation we
can find the other half of the co-ordinates.
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23. Example
Question: Draw the graph of 2x + y = 4
Solution
x = 0
2(0) + y = 4
y = 4
1st
Co-ordinate = (0,4)
y = 0
2x + 0 = 4
2x = 4
x = 2
2nd
Co-ordinate = (2,0)
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24. So the graph will look like this.
y
x1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
8
–
7 –
6 –
5 –
4 –
3 –
2 –
1 -
1
-
2
-
3
-
4
-
5
-
6
2x + y = 4
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25. Exercise
Plot the following graphs using the x=0, y=0 method.
1) x + y = 5
2) x + 2y = 2
3) 2x + 3y = 6
4) x + 3y = 3
Click to reveal plotted lines
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26. Answers
y
x1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
8
–
7 –
6 –
5 –
4 –
3 –
2 –
1 -
1
-
2
-
3
-
4
-
5
-
6
1. 3x + 2y = 6
2. x + 2y = 2
3. 2x + 3y = 6
4. x - 3y = 3
Click for further
exercises
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27. Exercise
1) x + y = 4
2) 2x + y = 2
3) x + 2y = 2
4) x + 3y = 6
5) 2x + 5y = 10
6) x – y = 3
7) 2x – y = 2
8) 2x – 3y = 6
9) x + 2y = 1
10) 2x – y = 3
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Using the x = 0, y = 0 method plot the following graphs:

28. What are the Co-ordinates of these points?
-1
1
-5
-4
-3
-2
5
4
3
2
1
-5 -4 -3 -2 0 2 3 54-1
(x,y)
Back to Main Page

29. Negative Numbers
(1) 2 + 3 (2) 6 - 5 (3) 3 - 7 (4) -2 + 6
(5) -1 - 2 (6) -4 + 5 (7) -2 - 2 (8) 0 – 4
(9) -3 + 6 (10) -4 - 1 (11) 6 - 8 (12) -5 - 2
(13) -8 + 4 (14) -5 - (- 2) (15) 0 - (- 1)
(16) 7 - 12 + 9 (17) -4 - 9 + -2 (18) 14 - (- 2)
(19) -45 + 17 (20) 4 - 5½
Addition and Subtraction
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30. Negative Numbers
(1) 4 x -3 (2) -7 x -2
(3) -5 x 4 (4) 28 ÷ -7
(5) -21 ÷ -3 (6) -20 ÷ 5
(7) -2 x 3 x 2 (8) -18 ÷ -3 x 2
(9) -2 x -2 x -2 (10) 2.5 x -10
Multiplication and Division
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31. Substituting Numbers into Formulae
Exercise
Substitute x = 4 into the following formulae:
1) x – 2
2) 2x
3) 3x + 2
4) 1 – x
5) 3 – 2x
6) 4 - 2x
7) x - 3
2
8) 3 - x
2
9) 2x – 6
Click forward to reveal answers
2
8
14
-3
-5
-4
-1
1
2
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32. Substituting Negative Numbers into Formulae
Exercise
Substitute x = -1 into the following formulae:
1) x – 2
2) 2x
3) 3x + 2
4) 1 – x
5) 3 – 2x
6) 4 - 2x
7) x - 3
2
8) 3 - x
2
9) 2x – 6
Click forward to reveal answers
-3
-2
-1
2
5
6
-3½
3½
-8
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