The document discusses straight line graphs and their equations. It states that all straight line graphs are of the form y = mx + c, where m is the gradient or slope and c is the y-intercept. Several examples of lines with different gradients and y-intercepts are shown, and their equations listed. The lines are then split into two groups based on whether their gradients are positive or negative.

1. 0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
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Straight Line Graphs
m gives the gradient of the line and c gives the y intercept.
All straight line
graphs are of the
form y = mx + c
The gradient is
defined as the
rise/run
rise = 2
run = 1
y intercept = 3
y = 2x + 3

2. 0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
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9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Straight Line Graphs
m gives the gradient of the line and c gives the y intercept.
All straight line
graphs are of the
form y = mx + c
The gradient is
defined as the
rise/run
rise = 3
run = 1
y intercept = -4
y = 3x - 4

3. 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
Straight Line Graphs
m gives the gradient of the line and c gives the y intercept.
All straight line
graphs are of the
form y = mx + c
The gradient is
defined as the
rise/run
rise = 1
run = 2
y intercept = 1
y = ½x + 1

4. 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
Straight Line Graphs
m gives the gradient of the line and c gives the y intercept.
All straight line
graphs are of the
form y = mx + c
The gradient is
defined as the
rise/run
rise = 1
run = 3
y intercept = -5
1
y = x -5
3

5. 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
Straight Line Graphs
m gives the gradient of the line and c gives the y intercept.
All straight line
graphs are of the
form y = mx + c
The gradient is
defined as the
rise/run
rise = 3
run = 4
y intercept = 2
3
y = x +2
4

6. Consider the straight lines shown below:
(a) (c)(b)
(d) (e)
Can you split the lines into two groups based on their gradients ?
Lines (a) (c) and (d) slope upwards from left to right.
Lines (b) and (e) slope downwards from left to right.
Positive
gradient
Negative
gradient

7. 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
Straight Line Graphs
m gives the gradient of the line and c gives the y intercept.
All straight line
graphs are of the
form y = mx + c
The gradient is
defined as the
rise/run
rise = 4
run = 5
y intercept = 3
4
y =- x +3
5

8. 1. y = 2x + 3
2. y = 3x – 5
3. y = -x + 6
4. Y = ½x –2
5. Y = - 4x –9
6. y = ¾x
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
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Determine the equations of the following lines
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