1. Straight Line Graphs

2. Sections 1)Horizontal, Vertical and Diagonal LinesHorizontal, Vertical and Diagonal Lines (Exercises) 2)y = mx + cy = mx + c ( Exercises : Naming a Straight LineNaming a Straight Line Sketching a Straight LineSketching a Straight Line) 3)Plotting a Straight Line - Table MethodPlotting a Straight Line - Table Method (Exercises) 4)Plotting a Straight Line – X = 0, Y = 0 MethodPlotting a Straight Line – X = 0, Y = 0 Method (Exercises) 5) Supporting Exercises Co-ordinatesNegative NumbersSubstitutionCo-ordinatesNegative NumbersSubstitution

3. x y 1 -5 -4 -3 -2 4 3 2 1 -5-4-3-202354 Naming horizontal and vertical lines (-4,-2)(0,-2)(2,-2) y = -2 (3,4) (3,1) (3,-5) x = 3 (x,y) Back to Main Page

4. 1 -5 -4 -3 -2 4 3 2 1 -5-4-3-202354 Now try these lines (-4,2)(0,2)(-4,2) y = 2 (-2,4) (-2,1) (-2,-5) x = -2 (x,y) Back to Main Page y x

5. -5 -4 -3 -2 4 3 2 1 1-5-4-3-202354 See if you can name lines 1 to 5 (x,y) 1 53 4 2 Back to Main Page y x y = 1 x = 1x = 5 y = -4 x = -4

6. 1 -5 -4 -3 -2 4 3 2 1 -5-4-3-202354 Diagonal Lines (-4,-3)(0,1)(2,3) (3,3) (1,1) (-3,-3) y = -x (x,y) Back to Main Page (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 4 3 2 1 -5-4-3-202354 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 Back to Main Page

9. y x 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 -2-2 -3-3 -4-4 -5-5 -6-6 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 Back to Main Page

10. y x 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 -2-2 -3-3 -4-4 -5-5 -6-6 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 Back to Main Page

11. y x 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 -2-2 -3-3 -4-4 -5-5 -6-6 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 y = x - 1 -2 1 y = -2x + 1 Back to Main Page

12. y x 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 -2-2 -3-3 -4-4 -5-5 -6-6 Exercise Back to Main Page 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 Back to Main Page

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! Back to Main Page x012 y135

15. The Table Method 0 1432-2-3-4 -2 -3 -4 1 2 3 4 y = 2x + 1 Back to Main Page x012 y 135

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 Back to Main Page x012 y

17. The Table Method 0 1432-2-3-4 -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 Back to Main Page 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. Back to Main Page

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. Back to Main Page

21. y x 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 -6 -5 -4 -3 -2 -1 -1 -2-2 -3-3 -4-4 -5-5 -6-6 This is where the graph cuts the y – axis (x=0) This is where the graph cuts the x – axis (y=0) Back to Main Page

22. By substituting these values into the equation we can find the other half of the co-ordinates. Back to Main Page

23. Example Question: Draw the graph of 2x + y = 4 Solution x = 0 2(0) + y = 4 y = 4 1 st Co-ordinate = (0,4) y = 0 2x + 0 = 4 2x = 4 x = 2 2 nd Co-ordinate = (2,0) Back to Main Page

24. So the graph will look like this. y x 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 -2-2 -3-3 -4-4 -5-5 -6-6 2x + y = 4 Back to Main Page

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 Back to Main Page

26. Answers y x 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 -1 -2-2 -3-3 -4-4 -5-5 -6-6 1.3x + 2y = 6 2.x + 2y = 2 3.2x + 3y = 6 4.x - 3y = 3 Click for further exercises Back to Main Page

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 Back to Main Page Using the x = 0, y = 0 method plot the following graphs:

28. What are the Co-ordinates of these points? 1 -5 -4 -3 -2 5 4 3 2 1 -5-4-3-202354 (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 Back to Main Page

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 Back to Main Page

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 2 Back to Main Page

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 2 5 6 -3½ 3½ -8 Back to Main Page