ICT linear Equation

posted by Mr Johari
This activity is an introduction on function, algebraic equation involving x and y and graphical representation of linear equation.
Approach: Individual or pair work using ICT graphical tools (Grapher or Geogebra)
Resource: ICT Linear Equation worksheet.


Task 1
Complete the given worksheet
section 1, 2, 3 and 4 and answer the corresponding questions given.

In a nutshell:
A. section 1: general for y=a
observation: horizontal straight lines and parallel to each other. No slope and all lines pass through the y-axis according to given equation. eg. line of equation y=2 passes y-axis at 2. The lines do not meet (intercept).

B. section 2: general for x=b
observation: vertical straight lines and parallel to each other. since the lines are all vertical the slope cannot be defined (no value can be given). The lines pass through the x-axis according to the given equation. eg. line of equation x= 4 passes x-axis at 4.

C. section 3: general for y=mx + c, c=0
observation: diagonal straight lines (or lines at an angle) that all converge or meet at the origin (the point where the x-axis meets the y-axis). Henc
e c refers to the point where the lines meet the y-axis (in this case c=0). When m is negative the lines slope downwards (bottom left to top right) and when m is positive the lines slope upwards (top left to bottom right). m is also known as the slope or gradient (refer to geographical concept of slope / gradient of rise and run)

D. section 4: general for y=mx + c
observation: diagonal lines as in section3 but m remains the same (m=2) but the lines meet the y-axis at different values. all lines are parallel (because m=2) but intersect (meet) the y-axis according to the value of c. i.e. if y=2x+4 the slope is positive and the y-intercept (where it meets the y-axis) is at 2.

E. section 5: general for y=mx + cobservation: diagonal lines as in section3 but c remains the same (c=1). The lines have the same intersection point (i.e. meet the y-axis at y=3) but have different slope or gradient.

Conclusion

Task 2
Refer to the link on
Graph (by GCSE Bitesize) to learn by graphical representation and plotting.
Leading questions for you to answer (post in your comment):
  1. what is a Cartesian Plane?
  2. what is ordinate? abscissa?
  3. give an example of a practical use of coordinate system (provide links to examples)
  4. a student was posed with the following problem 'A man Jim has twice the amount of money than his friend Lemin - present the above information as an equation in x and y and show a graphical representation of this equation'. show graphically how much will Lemin has if Jim has $4000.


5 comments:

  1. Please post your comments to TASK 2 here

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  2. 1. The Cartesian plane consists of two directed lines that perpendicularly intersect their respective zero points.

    2. The value of x is called the x-coordinate or abscissa and the value of y is called the y-coordinate or ordinate.

    3. For example, the point (24, 5) has an abscissa of 24, while the ordinate is 5.

    Link: http://www.tutorvista.com/math/abscissa-and-ordinate

    4. If Jim has $4000 which is twice of what Lemin have, then 1 line of a grid is one unit which is $2000, so the ordinate is at the mark 2 while the abscissa is at the mark 1. So the graph should intersect where the two lines meet.

    ReplyDelete
  3. 1. what is a Cartesian Plane?
    A Cartesian Plane is a plane with a rectangular coordinate system that associates each point in the plane with a pair of numbers.

    2. what is ordinate? abscissa?
    Ordinate refers to that element of an ordered pair which represents the distance traveled parallel to the vertical axis of a two-dimensional Cartesian coordinate system(y axis) while an abscissa is the x axis of a (2-D) Cartesian coordinate system.

    3. give an example of a practical use of coordinate system (provide links to examples)

    Example: To plot Q(4, –3) in the co–ordinate plane.

    Link:http://www.wonderwhizkids.com/Maths/Analytical+Geometry/Co-ordinate+axes/Co-ordinate+axes.html

    4. a student was posed with the following problem 'A man Jim has twice the amount of money than his friend Lemin - present the above information as an equation in x and y and show a graphical representation of this equation'. show graphically how much will Lemin has if Jim has $4000.

    We will take Jim as the x while we take Lemin as the y. If Jim has $4000, then the line will have to pass through the $4000 mark of the x axis and since Lemin has half lesser which is: 4000÷2=2000
    So, the line will have to pass through the $2000 mark of the y axis. Therefore, the line will pass through the $2000 mark of the y axis and pass through the mark of $4000 of the x axis.

    ReplyDelete
  4. The Cartesian plane consists of two directed lines that perpendicularly intersect their respective zero points.
    When 2 perpendicular number lines intersect, a Cartesian Plane is formed.


    Abscissa is known as the value of the X-coordinate or X- axis on a coordinate plane.
    It is a value of the horizontal axis on a coordinate plane.
    Ordinate is called as the value of the Y-coordinate or Y-axis on a coordinate plane.
    It is also the value of the vertical axis on a coordinate plane.


    For example of the many coordinate systems, but narrowed to the Cartesian coordinate system,here-http://www.answers.com/topic/coordinate-system

    If Jim has $4000 and Lemin with $2000 which is half of Jim's money, then 1 line of a grid can be a unit which is $2000 as the common factor is $2000, so the ordinate is at the mark 2, while the abscissa is at the mark 1. If all goes right, the lines should intercept.

    ReplyDelete
  5. 1. Two directed lines that intercept perpendicularly at their zero points.

    2. Abscissa is commonly known as the X-Axis or X-coordinate
    and Ordinate is commonly known as the Y-coordinate or Y-Axis

    3. http://bit.ly/9OOWQs This link provides a wide range of uses of the coordinate system in terms of computer programming.

    3. If Jim has $4000 and he has twice as much as Lemin, Lemin will have $2000 because taking Lemin's money as an unknown 'y', the expression will be y=4000/2. This way, the expression is simplified to y=2000 so the abscissa will stay in mark 1, and the ordinate will be at the 2nd mark. This gradient is 0.

    ReplyDelete