1. Drawing Linear Graphs Starter: Multiplying Negative Numbers (1) -3 x 4 = (4) -2 + 2 = (7) -6 x 4 + 4 = (10) -3 x 3 +9 = (13) 7 x -4 +2 = (16) 4 x -4 +9 = (19) -2 x -2 -2 = (2) 7 x 4 = (5) -3 x 4 = (8) -2 x -4 = (11) -2 x 8 -5 = (14) 3 x -7 = (17) -3 x 4 +6 = (20) -3 x 3 +3 = (3) -2 x 9 = (6) -4 x 5 = (9) -9 x 4 = (10) -5 x -4 +5 = (11) 9 x 3 -4 = (12) -2 x -2 + 2 = (13) -3 x -3 +3 = -1228-18 0-12 -20 8 -36 0-2125 -26-2123 -7 -21 6 2 -6 12

2. Drawing Linear Graphs Objective: Be able to draw linear graphs Outcomes Must: Substitute negative integers into function (positive gradients). Should: Draw linear graphs (positive gradients). Could: Sketch graphs

3. Drawing Graphs (positive gradients) Y = 2x + 1 x-20123 y -3 1 3 57 123 -2 2 4 6 8 10 -4 -2 Y = 2x + 2 x-20123 y 123 -2 2 4 6 8 10 -4 -2 02 4 68 2 x y x y

4. 123-2 5 10 15 -5 -10 x y (1) Y = 3x + 2 x-20123 y (2) Y = 2x + 5 x-20123 y (3) Y = 3x -3 x-20123 y (4) Y = 2x + 10 x-20123 y (5) Y = 4x + 1 x-20123 y -4 2 5 811 (1) Y = 3x + 2 1 35 7 911 (2) Y = 2x + 5 -9 -6-3 0 36 (3) Y = 3x-3 6 810 12 1418 (4) Y =2x+10 -7 -310 12 1418 (5) Y =4x+1 Starter:

5. 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 = x y = 2x y = 3x y = ½x x y 0  0 3  3 -4  -4 x y 0  0 3  6 -4  -8 x y 0  0 2  6 -3  -9 x y 0  0 8  4 4  2 Drawing Straight Line Graphs Use grid 1 to draw 4 graphs with me.

6. Drawing Graphs Y = 3x - 2 x-20123 y -8 -5-2 1 47 123-2 2 4 6 8 -6 -4 -8 Y = 2x - 4 x-20123 y 123 -2 2 4 6 8 -6 -4 -8 -5-2 1 47 x y x y

7. Drawing Linear Graphs Objective: Be able to draw linear graphs Outcomes Must: Substitute negative integers into function (negative gradients). Should: Plot the linear graphs (negative gradients). Could: Sketch graphs and understand the relationship between the positive and negative slope of the line

8. Drawing Graphs (negative gradients) Y = -2x + 1 x-20123 y 5 31 -3-5 123 -2 -4 2 4 6 -8 -6 Y = -2x + 2 x-20123 y x y 123 -2 -4 2 4 6 -8 -6 x y 6 42 0 -2-4

10. 123-2 5 10 15 -5 -10 x y (1) Y = -3x + 2 x-20123 y (2) Y = -2x + 5 x-20123 y (3) Y = -3x -3 x-20123 y (4) Y = -2x + 10 x-20123 y (5) Y = -4x + 1 x-20123 y 8 52 -4-7 9 75 3 1 3 0-3 -6 -9-12 14 1210 8 64 9 51 -3 -7-11

11. 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 = -x y = -2x y = -3x + 4 y = -½x - 3 x y 0  0 5  -5 -6  6 x y 0  0 3  -6 -5  10 0  4 4  -8 -2  10 0  -3 8  -7 -8  1 x y

12. Sketching Graphs Learning Objective: Sketching Graphs without a table of values

13. Sketching Graphs Y = x + 3 Y = -x + 2 The sign in front of the x tells you if the gradient is positive or negative. Positive gradient Negative gradient This tells you where the line cuts the vertical line 3 cuts the vertical line at 2 2

14. Gradient The Gradient is the slope. The steeper the slope of the line the lare the value of the gradient: Gradient= Distance Measured UP Distance Measured Along Dif of the Y Dif of the X

15. Drawing Graphs 123 -2 -4 2 4 6 -8 -6 x y 123 -2 -4 2 4 6 -8 -6 x y Dif of the Y Dif of the X

16. 1. y = x + 5 2. y = x + 1 3. y = x + 3 4. y = x - 6 5. y = x - 5 6. y = x - 1 7. y = -x + 7 8. y = -x + 3 9. y = -x - 4 10. y = 2x + 5 Starter: sketch the graph of each of the equation. 5 1. 1 2. 3 3. -6 4. -5 5. 6. 3 8. -4 9. 7 7. 5 10.