drawing linear graphs starter: multiplying negative numbers (1) -3 x 4 = (4) -2 + 2 = (7) -6 x 4 + 4...
TRANSCRIPT
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 =
-12 28 -18
0 -12 -20
-20 8 -36
0 -21 25
-26 -21 23
-7 -21 6
2 -6 12
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
Drawing Graphs (positive gradients)Y = 2x + 1
x -2 -1 0 1 2 3
y -3 -1 1 3 5 7
1 2 3-1-2
2
4
6
8
10
-4
-2
Y = 2x + 2
x -2 -1 0 1 2 3
y
1 2 3-1-2
2
4
6
8
10
-4
-2
-2 0 2 4 6 8
2
x
y
x
y
1 2 3-1-2
5
10
15
-5
-10
x
y(1) Y = 3x + 2
x -2 -1 0 1 2 3
y
(2) Y = 2x + 5
x -2 -1 0 1 2 3
y
(3) Y = 3x -3
x -2 -1 0 1 2 3
y
(4) Y = 2x + 10
x -2 -1 0 1 2 3
y
(5) Y = 4x + 1
x -2 -1 0 1 2 3
y
-4 -1 2 5 8 11
(1) Y = 3x + 2
1 3 5 7 9 11
(2) Y = 2x + 5-9 -6 -3 0 3 6
(3) Y = 3x-3
6 8 10 12 14 18
(4) Y =2x+10
-7 -3 10 12 14 18
(5) Y =4x+1
Starter:
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-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.
Drawing GraphsY = 3x - 2
x -2 -1 0 1 2 3
y -8 -5 -2 1 4 7
1 2 3-1-2
2
4
6
8
-2
-6
-4
-8
Y = 2x - 4
x -2 -1 0 1 2 3
y
1 2 3-1-2
2
4
6
8
-2
-6
-4
-8
-8 -5 -2 1 4 7
x
y
x
y
Drawing Linear GraphsObjective: Be able to draw linear
graphsOutcomes
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
Drawing Graphs (negative gradients)Y = -2x + 1
x -2 -1 0 1 2 3
y 5 3 1 -1 -3 -5
1 2 3-1-2-2
-4
2
4
6
-8
-6
Y = -2x + 2
x -2 -1 0 1 2 3
y
x
y
1 2 3-1-2-2
-4
2
4
6
-8
-6
x
y
6 4 2 0 -2 -4
1 2 3-1-2
5
10
15
-5
-10
x
y(1) Y = -3x + 2
x -2 -1 0 1 2 3
y
(2) Y = -2x + 5
x -2 -1 0 1 2 3
y
(3) Y = -3x -3
x -2 -1 0 1 2 3
y
(4) Y = -2x + 10
x -2 -1 0 1 2 3
y
(5) Y = -4x + 1
x -2 -1 0 1 2 3
y
8 5 2 -1 -4 -7
9 7 5 3 1 -1
3 0 -3 -6 -9 -12
14 12 10 8 6 4
9 5 1 -3 -7 -11
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-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
x y
Sketching Graphs
• Learning Objective:
Sketching Graphs without a table of values
Sketching Graphs
Y = x + 3Y = -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
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
Drawing Graphs
1 2 3-1-2-2
-4
2
4
6
-8
-6
x
y
1 2 3-1-2-2
-4
2
4
6
-8
-6
x
y
Dif of the YDif of the X
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.
51.
1
2. 3
3.
-6
4.
-5
5.
-1
6.
3
8.
-4
9.
77.
510.
