Linear Graph/Equation (Quiz4/5 solution)

Quiz 4 (Solution)

Quiz 5 Solution

Linear Equation (Graph) reference

posted by Mr Johari

reference of Linear Equation. (click here)
Focuses on

• What is linear equation?
• Plotting and Table of Values
• Slope / Gradient of a Line
• Slope and y-intercept (how to form a Linear Equation)

linear Graph part 2

posted by Mr Johari

source: http://www.math.com/school

This is a supplementary note that focuses on linear equation:

Part 2: Graphing Linear Equation (Exercise)

Complete the 2 exercises, state your answers as comments. Where possible justify your answers with simple working.

Question 1: focuses on the linear graph of the form y = mx + c
Question 2: focuses on the characteristics of the linear graph.

[Coordinate, gradient/slope, intercept, equation]

Linear Graph part 1

posted by Mr Johari
source: http://www.math.com/school/subject2/lessons/S2U4L3DP.html

This is a supplementary note that focuses on plotting of a linear equation:

Part 1: Graphing Linear Equation

Method 1: Given linear equation, plot the graph.

Technique: Using plotting points and coordinates. (i.e. identify any points for x and find corresponding values of y for plotting)

Method 2: Given linear equation, plot the graph.

Technique: Using gradient and y-intercept

Form the general linear equation ie. y=mx+c, where m is the gradient and c is the y-intercept.

Exercise: (for self practice - answer provided)

Given a linear line, find the equation of the line.

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 + c
observation: 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.
activity 1: learn about coordinate system

Leading questions for you to answer (post in your comment):
reference: Cartesian Plane and Descartes

1. what is a Cartesian Plane?
2. what is ordinate? abscissa? what is the significance of (x,y)
   
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.

Task 3

In the following task, you are required to use Geogebra.

You are provided with the graph of y against x.
A linear graph has been plotted with the equation unknown.
Please comment on the following:
(1) the shape of the graph
(2) the possible equation of this linear graph (other than y=2x)