1. DRAWING GRAPHS FROM EQUATIONS

2. Objectives  Learn how to calculate coordinates specific to an equation  Learn how to draw a graph of any equation

3. Key points Make sure your pencil is sharp Restrict use of eraser Work out your coordinates Work out your scale, be consistent! Label axis Join points with ruler Label the line Give your graph a title

4. Drawing Graphs from Equations A graph can be drawn from any equation. For example, draw the graph of: y = 2x This means double x

5. To draw the graph of y = 2x draw a table like this putting in any numbers for the values for x x -4-2024

6. x -4-2024 2x -8-4048 I want to find y = 2x, so for every value of x we multiply by 2 for 2 x.

7. x -4-2024 2x -8-4048 y -8-4048 You have multiplied all the x numbers so now you have found the corresponding y numbers for y = 2x

8. x -4-2024 y -8-4048 Now you have your set of coordinates you are ready to plot the graph (-4,-8) (-2,-4) (0,0) (2,4) (4,8)

9. 0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 y = 2x x y 0  0 2  -4 -4  -8 -2  4  4 8 y = 2x Graph of equation y = 2x

10. Drawing Graphs from Equations Now lets draw the graph of: y = 2x + 1 This means double x and then add 1

11. First put in your x coordinates x -4-2024

12. x -4-2024 2x -8-4048 I want to find y = 2x + 1, so first, you find the value of the 2x. This means 2 multiplied by x

13. x -4-2024 2x -8-4048 2x + 1 -7-3159 add on 1 to the 2x Remember, you want to find y = 2x + 1 so you add on 1 to the 2x to find the value of 2x + 1

14. x -4-2024 2x -8-4048 2x + 1 -7-3159 y -7-3159 Now you have the coordinates for y = 2x + 1

15. x -4-2024 y -7-3159 Now, plot the value of x against the value of y on the graph’s axes.

16. 0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 y = 2x + 1 x y -4  1 2  -3 -7 4  0  -2  5 9 y = 2x + 1 Graph of equation y = 2x + 1

17. x -4-2024 Draw the graph of: y = -½x - 3

18. Find the value of -½x. You times all the x numbers by -½ x -4-2024 -½x 210-2 Draw the graph of: y = -½x - 3

19. Take away 3 from the value of -½x. x -4-2024 -½x 210-2 -½x - 3 -2-3-4-5 Draw the graph of: y = -½x - 3

20. Now you can plot your graph x -4-2024 -½x 210-2 -½x - 3 -2-3-4-5 y -2-3-4-5 Draw the graph of: y = -½x - 3

21. Now you can plot your graph x -4-2024 y -2-3-4-5 Draw the graph of: y = -½x - 3

22. 0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 y = -½x - 3 0  -3 2  -2 -4  -5 4  -2  -4 x y Graph of equation y = -½x - 3 y = -½x - 3

23. Equations of lines with only one letter  You have learnt how to draw any line of equations in the form of y = 2x + 3  What about equations where there is only 1 letter?  y = 1  x = 5

24. (1, 3) (1, –1 ) (1, 5) (1, –4) What do they all have in common? An x value equal to 1 They also all lie in line If we labelled some more points on the line, what would they have in common with these? They would also have an x value equal to 1 (1, –3) (1, 0) (1, 1) We can therefore say the equation of the line is x = 1 Equations of lines with only one letter  Consider the points shown on the graph

25. Consider the points shown on this graph (2, 3) (0, 3) (5, 3) (-2, 3) What do they all have in common? A y value equal to 3 If we labelled some more points on the line, what would they have in common with these points? They would also have a y value equal to 3 (-5, 3) (3, 3) (-4, 3) We can therefore say the equation of the line is y = 3 They also all lie in line

26. 0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 Lines that cut the y axis Y = 8 Y = 4 Y = 2 Y = 0 Y = -3 Y = -8 Lines that cut the x axis x = 9 x = 0 x = 5 x = - 4 x = - 7

27. 0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 1.y = 2x + 3 2.y = 3x – 5 3.y = -x + 6 4.y = -4 5.x = 7 6.Y = ½x –2 7.Y = - 4x -9 Work!! Plot the following graphs