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
4) Plotting a Straight Line – X = 0, Y = 0 Method
5) Supporting Exercises
Co-ordinates Negative Numbers Substitution

3. Naming horizontal and vertical linesy 1 -5 -4 -3 -2 -1 4 3 2 5
(x,y)
(3,4)
(3,1) x
y = -2
(-4,-2)
(0,-2)
(-4,-2)
(3,-5)
x = 3
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4. Now try these lines y (x,y) (-2,4) y = 2 (-2,1) x (-4,2) (0,2) (-4,2)-5 -4 -3 -2 -1 4 3 2 5
(x,y)
(-2,4)
y = 2
(-2,1) x
(-4,2)
(0,2)
(-4,2)
(-2,-5)
x = -2
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5. See if you can name lines 1 to 5
(x,y) y
x = 1
x = 5 4
x = -4 3 2
y = 1 1 1 x -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3
y = -4 4 -4 -5 5 2 3
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6. Diagonal Lines (x,y) y y = x (-3,3) (3,3) (-1,1) (1,1) x (2,-2)-5 -4 -3 -2 -1 4 3 2 5
y = x
(-3,3)
(3,3)
(-1,1)
(1,1) x
(2,-2)
(-3,-3)
(-4,-3)
(0,1)
(2,3)
y = -x
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7. Now see if you can identify these diagonal lines
y = x + 1 1 -5 -4 -3 -2 -1 4 3 2 5 3
y = x - 1
y = - x - 2 x
y = -x + 2 4 1 2
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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.
c is known as the intercept
y = mx + c
m is known as the gradient
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9. y x Finding m and c Find the Value of c 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.
So c = 3
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.
y = 2x +3
y = mx +c
So m = 2
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10. y x Finding m and c Find the Value of c 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.
y = mx +c
y = 2x +3
So c = 2
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.
So m = -1
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11. y x Some Lines to Identify 1 2 y = x + 2 1 -1 y = x - 1 -2 1 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: 1 2
y = x + 2
Line 2
m =
c =
Equation: 1 -1
y = x - 1
Line 3
m =
c =
Equation: -2 1
y = -2x + 1
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12. y x Exercise 5 Click for Answers 1) y = x - 2 3 2) y = -x + 3 1 2 3 4 5 6 7 8
–7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6 5
Click for Answers 3
1) y = x - 2
2) y = -x + 3
3) y = 2x + 2
4) y = -2x - 1
y = -2x - 1 2 2 1 4
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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
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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 = y = 2(0) y = 1 x 1 2 y 3 5
x = y = 2(1) y = 3
x = y = 2(2) y = 5
Now you just have to plot the points on to a graph!
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15. The Table Method x 1 2 y 1 3 5 4 3 2 1 -4 -3 -2 -1 1 2 3 4 -1 -21 2 y 4 3 1 3 5 2 1 -4 -3 -2 -1 1 2 3 4 -1 -2
y = 2x + 1 -3 -4
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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 x 1 2 y
Click to reveal plotted lines
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17. The Table Method 4 3 2 1 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 3 1 -4 4 21 2 3 4 -1 -2 -3 3 1
Click for further
exercises -4 4 2
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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 2
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19. The x = 0, y = 0 Method
This method is used when x and y are on the same side. Example: x + 2y = 4
To draw a straight line we only need 2 points to join together.
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20. If we find the 2 points where the graph cuts the axes then we can plot the line.
These points are where x = 0 (anywhere along the y axis) and y = 0 (anywhere along the x axis).
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21. y x 8 7 6 5 This is where the graph cuts the x – axis (y=0) 4 3 1 2 3 4 5 6 7 8 -1 -2 -3 -4 -5 -6
This is where the graph cuts the x – axis (y=0)
This is where the graph cuts the y – axis (x=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
1st Co-ordinate = (0,4)
y = 0
2x + 0 = 4
2x = 4
x = 2
2nd Co-ordinate = (2,0)
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24. y x So the graph will look like this. 2x + y = 4 1 2 3 4 5 6 7 8 1 2 3 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.
Click to reveal plotted lines
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26. y x Answers 3x + 2y = 6 x + 2y = 2 2x + 3y = 6 x - 3y = 3 1 2 3 4 5 6 7 8
–7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6
Answers
3x + 2y = 6
x + 2y = 2
2x + 3y = 6
x - 3y = 3
Click for further
exercises
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27. Exercise Using the x = 0, y = 0 method plot the following graphs:
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28. What are the Co-ordinates of these points?-1 1 -5 -4 -3 -2 5 4 3 2
(x,y)
Mention the order of cartesian co-ordiantes (x is a-cross)
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29. Negative Numbers (1) 2 + 3 (2) 6 - 5 (3) 3 - 7 (4) -2 + 6
Addition and Subtraction
(1) (2) (3) (4)
(5) (6) (7) (8) 0 – 4
(9) (10) (11) (12)
(13) (14) (- 2) (15) (- 1)
(16) (17) (18) 14 - (- 2)
(19) (20) 4 - 5½
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30. Negative Numbers (1) 4 x -3 (2) -7 x -2 (3) -5 x 4 (4) 28 ÷ -7
Multiplication and Division
(1) x -3 (2) -7 x -2
(3) x 4 (4) 28 ÷ -7
(5) ÷ -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
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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 2 8 14 -3 -5
6) x
7) x - 3 2
8) x
9) 2x – 6 -4 -1 1 2
Click forward to reveal answers
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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 -3 -2 -1 2 5
6) x
7) x - 3 2
8) x
9) 2x – 6 6
-3½ 3½ -8
Click forward to reveal answers
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