CHAPTER 5 The Straight Line

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CHAPTER 5The Straight Line
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Learning Objectives

• 5.1 Understand the concept of gradient of a
  straight line.
• 5.2 Understand the concept of gradient of a
  straight line in Cartesian coordinates.
• 5.3 Understand the concept of intercept.
• 5.4 Understand and use equation of a straight
  line.
• 5.5 Understand and use the concept of parallel
  lines.

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5.1 GRADIENT OF A STRAIGHT LINE

• (A) Determine the vertical and horizontal
  distances between two given points on a straight
  line

F
E
G

• Example of application AN ESCALATOR.
• EG - horizontal distance(how far a person goes)
• GF - vertical distances(height changed)

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Example 1

• State the horizontal and vertical distances for
  the following case.

10 m
16 m
Solution The horizontal distance 16 m The
vertical distance 10 m
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(B)Determine the ratio of the vertical distance
to the horizontal distance
10 m
16 m

• Let us look at the ratio of the vertical
  distance to the horizontal distances of the slope
  as shown in figure.

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• Vertical distance 10 m
• Horizontal distance 16 m
• Therefore,
• Solution

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5.2 GRADIENT OF THE STRAIGHT LINE IN CARTESIAN
COORDINATES

• Coordinate T (X2,Y1)
• horizontal distance
• PT
• Difference in x-coordinates
• x2 x1
• Vertical distance
• RT
• Difference in y-coordinates
• y2 y1

y
R(x2,y2)
y2 y1
x2 x1
T(x2,y1)
P(x1,y1)
x
0
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Solution
REMEMBER!!! For a line passing through two points
(x1,y1) and (x2,y2), where m is the gradient
of a straight line
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• Example 2
• Determine the gradient of the straight line
  passing through the following pairs of points
• P(0,7) , Q(6,10)
• L(6,1) , N(9,7)
• Solution

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• (C) Determine the relationship between the value
  of the gradient and the
• Steepness
• Direction of inclination of a straight line
• What does gradient represents??
• Steepness of a line with respect to the x-axis.

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B

• a right-angled triangle. Line AB is a slope,
  making an angle with the horizontal line AC

C
A
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When gradient of AB is positive When gradient of AB is negative
y
y
B
B
x
x
0
0
A
A

• inclined upwards
• acute angle
• is positive

• inclined downwards
• obtuse angle.
• is negative

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Activity Determine the gradient of the given
lines in figure and measure the angle between the
line and the x-axis (measured in anti-clocwise
direction)
y
Line Gradient Sign
MN
PQ
RS
UV
N(3,3)
V(1,4)
Q(-2,4)
S(-3,1)
x
0
M(-2,-2)
R(3,-1)
P(2,-4)
U(-1,-4)
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• REMEMBER!!!
• The value of the gradient of a line
• Increases as the steepness increases
• Is positive if it makes an acute angle
• Is negative if it makes an obtuse angle

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Lines Gradient
AB 0



y
A
B
x
0
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Lines Gradient

CD Undefined


y
D
C
x
0
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Lines Gradient


EF Positive

y
F
E
x
0
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Lines Gradient



GH Negative
y
H
G
x
0
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Lines Gradient
AB 0
CD Undefined
EF Positive
GH Negative
y
D
H
F
A
B
G
E
C
x
0
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5.3 Intercepts
y-intercept
x-intercept

• Another way finding m, the gradient

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5.4 Equation of a straight line

• Slope intercept form
• y mx c
• Point-slope form
• given 1 point and gradient
• given 2 point

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5.5 Parallel lines

• When the gradient of two straight lines are
  equal, it can be concluded that the two straight
  lines are parallel.

Example Is the line 2x-y6 parallel to line
2y4x3?

• Solution
• 2x-y6y y2x-6 gradient is 2.
• 2y4x3 gradient is
  2.
• Since their gradient is same hence they are
  parallel.