Unit 28 Straight Lines

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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
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Unit 28

• 28.1 Positive and Negative Gradient

3
y
B
y
5
4
3
2
1

-1
-2
-3
-4
-5










A
x
Example Find the gradient of the line shown
opposite. Solution
-4 -3 -2 -1 0 1 2 3
x
Vertical change 10
Horizontal change 6
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4
y
B
y
5
4
3
2
1





A
A
x
(-2, 4)
Example Find the gradient of the line shown
opposite. Solution
B
(4, 1)
x
-2 -1 0 1 2 3 4
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Unit 28

• 28.2 Gradient of Perpendicular Lines

6
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).
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Solution
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Unit 28

• 28.3 Application of Graphs

8
Distance-time graph
Distance
The gradient gives the velocity. If the gradient
is zero, the object is not moving.
Time
2000
1500
1000
500
0
Example The graph shows the distance travelled
by a girl on bicycle. Find the speed she is
travelling on each stage of the journey








E
C
Distance (m)
D
B
A
50 100 150 200 250 300 350 400
Time (s)
Solution
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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.
Velocity
Time
8
7
6
5
4
3
2
1
Example The graph shows how the speed of a bird
varies as it flies between two trees. How far
apart are the two trees?








Velocity (m/s)
36m
B
A
C
6m
18m
2 4 6 8 10 12 14
Time (s)
Solution The distance is given by the area under
the graph, which can be split into 3 sections A,
B and C
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Unit 28

• 28.4 Equation of a Straight Line

11
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
y
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10
8
6
4
2
A
?
?
(-1, 9)
G
?
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B
?
(3, 1)
x
O
-3 -2 -1 0 1 2 3 4 5 6
?
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12
(c) Coordinates of G so (d) Equation of
line through O, the origin, perpendicular to
AB Equation i.e. (e) Equation of line
through O, parallel to AB Equation
i.e.
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y






10
8
6
4
2
A
?
(-1, 9)
G
?
?
?
?
B
(3, 1)
x
?
O
-3 -2 -1 0 1 2 3 4 5 6
?
?
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