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Unit 28Straight Lines
Presentation 1 Positive and Negative Gradient
Presentation 2 Gradients of Perpendicular Lines
Presentation 3 Application of Graphs
Presentation 4 Equation of Straight Line
Unit 2828.1 Positive and Negative
Gradient
A
B
Example
Find the gradient of the line shown opposite.
Solution
-4 -3 -2 -1 0 1 2 3
5
4
3
2
1
-1
-2
-3
-4
-5
y
x
?
?
?
?
Vertical change = 10
Horizontal change = 6
x
y
A
B
Example
Find the gradient of the line shown opposite.
Solution
x
y
-2 -1 0 1 2 3 4
5
4
3
2
1
A
B
(-2, 4)
(4, 1)
??
?
?
?
x
y
Unit 2828.2 Gradient of Perpendicular
Lines
?
If two lines are perpendicular to one another, then the product of the two gradients is equal to -1.
So if is the gradient of one line , the other line has a
gradient of
Example
Show that the line segment joining the points A(3, 2) and B(5, 7) is perpendicular to the line segment joining the points P(2, 5) and Q(7, 3).
Solution?
??
?
?
??
?
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Unit 2828.3 Application of Graphs
Distance-time graph
Distanc
e
Time
The gradient gives the velocity.If the gradient is zero, the object is not moving.
2000
1500
1000
500
0 50 100 150 200 250 300 350 400
Example
The graph shows the distance travelled by a girl on bicycle.
Find the speed she is travelling on each stage of the journey
Solution?
?
??
?
??
?
?
A
B
C
D
E
Time (s)
Distance (m
)
Solution
The distance is given by the area under the graph, which can be split into 3 sections A, B and C
Velocit
y
Time
velocity-time graph
The gradient gives the acceleration.If the gradient is zero, the object is moving at a constant velocity.The area under this graph is the distance travelled.
8
7
6
5
4
3
2
1
2 4 6 8 10 12 14
Example
The graph shows how the speed of a bird varies as it flies between two trees. How far apart are the two trees?A B C18m 36m 6m
?? ? ???? ???
Time (s)
Velocity (m
/s)
Unit 2828.4 Equation of a Straight Line
The equation a of a straight line is usually written in the form
Where m is the gradient and c is the intercept.
Example
(a)
(b) Equation of line AB:
As it passes through (3, 1)
and
10
8
6
4
2
-3 -2 -1 0 1 2 3 4 5 6
A
B
G
x
y
?
??
?
?(-1, 9)
(3, 1)
?
??
???
? ??
O
10
8
6
4
2
-3 -2 -1 0 1 2 3 4 5 6
A
B
G
x
y
(-1, 9)
(3, 1)
(c) Coordinates of G: so
(d) Equation of line throughO, the origin, perpendicularto AB:
Equation:
i.e.
(e) Equation of line through O, parallel to AB
Equation:
i.e.
?
?
?
O
??
?
??
?
??