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    Form 4 Chapter 5 Straight Line

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    GaryBong
    This chapter discusses straight lines. It defines gradient as the ratio of the vertical to horizontal distance between two points on a line. The gradient of a line in Cartesian coordinates is defined as (y2-y1)/(x2-x1). Parallel lines have the same gradient. The equation of a straight line can be written in slope-intercept form as y=mx+c, where m is the gradient and c is the y-intercept.

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    Form 4 Chapter 5 Straight Line

    Uploaded by

    GaryBong
    4K views23 pages
    This chapter discusses straight lines. It defines gradient as the ratio of the vertical to horizontal distance between two points on a line. The gradient of a line in Cartesian coordinates is defined as (y2-y1)/(x2-x1). Parallel lines have the same gradient. The equation of a straight line can be written in slope-intercept form as y=mx+c, where m is the gradient and c is the y-intercept.

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    This chapter discusses straight lines. It defines gradient as the ratio of the vertical to horizontal distance between two points on a line. The gradient of a line in Cartesian coordinates is defined as (y2-y1)/(x2-x1). Parallel lines have the same gradient. The equation of a straight line can be written in slope-intercept form as y=mx+c, where m is the gradient and c is the y-intercept.

    Copyright:

    © All Rights Reserved
    Download as PPT, PDF, TXT or read online from Scribd
    Download as ppt, pdf, or txt
    4K views23 pages

    Form 4 Chapter 5 Straight Line

    Uploaded by

    GaryBong
    This chapter discusses straight lines. It defines gradient as the ratio of the vertical to horizontal distance between two points on a line. The gradient of a line in Cartesian coordinates is defined as (y2-y1)/(x2-x1). Parallel lines have the same gradient. The equation of a straight line can be written in slope-intercept form as y=mx+c, where m is the gradient and c is the y-intercept.

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    © All Rights Reserved
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    Download as ppt, pdf, or txt
    of 23

    CHAPTER 5

    The Straight
    Line
    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.
    y2  y1
    m
    x2  x1
    y  mx  c
    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)


    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
    (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.
    Vertical distance = 10 m
    Horizontal distance = 16 m

    Therefore,
    Solution:

    vertical distance 16

    horizontal distance 10
     1.6
    5.2 GRADIENT OF THE STRAIGHT LINE IN
    CARTESIAN COORDINATES
    y • Coordinate T = (X2,Y1)
    • horizontal distance
    R(x2,y2)
    = PT
    = Difference in x-coordinates
    y2 – y1
    = x2 – x 1
    x2 – x 1 • Vertical distance
    P(x1,y1) T(x2,y1)
    = RT
    x = Difference in y-coordinates
    0
    = y 2 – y1
    Solution:
    vertical distance
    gradient of PR 
    horizontal distance
    RT

    PT
    y 2  y1

    x2  x1

    REMEMBER!!!
    For a line passing through two points (x1,y1) and (x2,y2),
    y2  y1
    m
    x2  x1
    where m is the gradient of a straight line
    Example 2
    • Determine the gradient of the straight line
    passing through the following pairs of points
    i) P(0,7) , Q(6,10)
    ii)L(6,1) , N(9,7)
    Solution:
    10  7 7 1
    Gradient PQ  Gradient LN 
    60 96
    3 units 6 units
     
    6 units 3 units
    1 2

    2
    (C) Determine the relationship between
    the value of the gradient and the

    (i)Steepness
    (ii)Direction of inclination of a straight line

    • What does gradient represents??


    Steepness of a line with respect to the x-
    axis.
    Activity:
    Determine the gradient of the given lines in figure
    and measure the angle between the line and the x-
    axis (measured
    y in anti-clocwise direction)

    Line Gradient Sign 


    V(1,4) N(3,3)
    Q(-2,4)
    MN
    S(-3,1)

    0
    x PQ
    M(-2,-2)
    R(3,-1) RS
    U(-1,-4)
    P(2,-4)
    UV
    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


    Lines Gradient
    y

    AB 0
    A B

    0 x
    Lines Gradient
    y

    CD Undefined
    C

    0 x
    Lines Gradient
    y

    EF Positive
    0 x
    Lines Gradient
    y

    0 x

    GH Negative
    Lines Gradient
    y

    D
    H
    F
    AB 0
    A B

    G
    CD Undefined
    E C
    EF Positive
    0 x

    GH Negative
    5.3 Intercepts

    y-intercept

    x-intercept

    • Another way finding m, the gradient:


    y - intercept
    m
    x - intercept
    5.4 Equation of a straight line
    • Slope intercept form
    y = mx + c

    • Point-slope form
    given 1 point and gradient:
    y  y1  m( x  x1 )
    given 2 point:
    y  y1 y 2  y1

    x  x1 x2  x1
    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-y=6 parallel to line 2y=4x+3?
    Solution:
    2x-y=6yy=2x-6 gradient is 2.
    3
    2y=4x+3 y  2x  gradient is 2.
    2
    Since their gradient is same hence they are parallel.
    y=x-2

    x -3 -2 -1 0 1 2 3
    y -5 -4 -3 -2 -1 0 1

    y=x+2

    x -3 -2 -1 0 1 2 3
    y -1 0 -3 2 3 4 5

    y = 2x + 4

    x -3 -2 -1 0 1 2 3
    y -2 0 2 4 6 8 10
    y
    y = 2x +4

    y = x +2

    y = x -2

    4
    2

    2 x
    -2
    -2

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