Introduction to Linear Functions and Graphs

Lew W. S., Marta Ruiz, Apr 15, 2025

This book is for self directed learning of graphs of linear functions

Table of Contents

  1. Introduction to Concept of Functions
    1. What is a function
    2. Function Machine
    3. Introduction to Cartesian Coordinate System
    4. A linear function's Input x and output y values on a Cartesian Coordinate System
    5. Input and Output of Graphs of Linear Functions
    6. Number Trick : Deducing the Algebraic Expression Behind the Trick
    7. Function Machine (with substitution of values shown)
  2. Graphing Linear Functions
    1. Linear Functions : Input Variable x and Output Variable y
    2. Graphing Linear Functions (Math Antics on You Tube)
    3. Graphing Linear Functions (II)
  3. Concept of Gradient
    1. Gradient (Slope): Intuitive Introduction
    2. Gradient (Slope) : Dynamic Illustration
    3. Gradient(Slope) Introductory videos on You Tube
    4. Game on Gradients of Straight Lines
    5. Quiz on Slope (3) | 斜率測驗(3)
    6. Quiz on Slope (2) | 斜率測驗(2)
    7. Quiz on Slope (1) | 斜率測驗(1)
    8. Quiz on Gradient of Line (1)
    9. Quiz on Gradient : Calculation of gradient
    10. Gradient of Line Self Quiz
    11. ACCESS - Slope Exercises
  4. Functions in Gradient Intercept form y = mx + c
    1. Relating a Linear Graph to its equation(function) in gradient and intercept form
    2. Gradient and Y Intercept of Straight Line & its Equation
    3. Steps in Finding Equation of Straight Lines 求直線方程的步驟
    4. Self Review on gradient and y intercept for y = mx + c, ax + by = c, ax + by + c = 0
    5. Reading Slopes from Equation of Straight Lines 由直線方程讀取斜率
    6. Gradient Intercept Form of Equation of line (linear function)
    7. Exploring the linear graph of y = m x + c
    8. 4Q Quiz: Graphing Linear Equations; Identifying Slope & y-intercept (With Hints)
    9. Graphing Linear Equations; Identifying Slope & y-intercept (With Hints)
    10. Graphing a Given Linear Equation (Self Practice)
    11. Linear (Straight Line) Graphs - Different forms of equation
    12. Equation of a Straight Line Given Linear Graph (Practice)
  5. Application of linear graphs in real world contexts
    1. Distance Time Graph ( in metres and seconds)
    2. Temperature Graph with Thermometer Display
    3. Linear Function Contextual Problems : Cost of T Shirts
    4. Linear Function Contextual Problems : Cost of Printing Cards

1.

Introduction to Concept of Functions

  • 1. What is a function
  • 2. Function Machine
  • 3. Introduction to Cartesian Coordinate System
  • 4. A linear function's Input x and output y values on a Cartesian Coordinate System
  • 5. Input and Output of Graphs of Linear Functions
  • 6. Number Trick : Deducing the Algebraic Expression Behind the Trick
  • 7. Function Machine (with substitution of values shown)

1.1.

What is a function

[size=150][size=200]Alternative videos to explain what is a function ?[br][br]What is a Function?[br][url=https://youtu.be/22A4KMU7-uo]https://youtu.be/22A4KMU7-uo[/url] (3m59s)[br][br]Meat-A-Morphosis: An Introduction to Functions[br][url=https://youtu.be/VUTXsPFx-qQ]https://youtu.be/VUTXsPFx-qQ[/url] (7m45s)[br][br]Algebra Basics: What Are Functions? - Math Antics[br][url=https://youtu.be/52tpYl2tTqk]https://youtu.be/52tpYl2tTqk[/url] (11m33s)[br][br][br][br][/size][/size]
[size=150][size=200]See an alternative function machine that processes patterns, numbers and simple equations.[br][br][url=https://phet.colorado.edu/sims/html/function-builder/latest/function-builder_en.html]https://phet.colorado.edu/sims/html/function-builder/latest/function-builder_en.html[/url][/size][/size]
– Cristina Masotta, Lew W. S.

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1.4.

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1.5.

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1.6.

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1.7.

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2.

Graphing Linear Functions

  • 1. Linear Functions : Input Variable x and Output Variable y
  • 2. Graphing Linear Functions (Math Antics on You Tube)
  • 3. Graphing Linear Functions (II)

2.1.

Linear Functions : Input Variable x and Output Variable y

Assess yourself if you understood the concept of linear functions, where it involves two variables x and y.[br][br]For example y = x + 4 is a linear function. [br]We can also refer to y as a function of x, where y = x + 4.[br]The concept of x as a variable where input values are used to replace x, [br]and the concept of y as the variable that contain the output values calculated based on the "rule" or y = x + 4 is being reinforced in the practice here. [br][br]Fill in the correct corresponding values of y and x for the given values of x and y.
– Lew W. S.

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3.

Concept of Gradient

  • 1. Gradient (Slope): Intuitive Introduction
  • 2. Gradient (Slope) : Dynamic Illustration
  • 3. Gradient(Slope) Introductory videos on You Tube
  • 4. Game on Gradients of Straight Lines
  • 5. Quiz on Slope (3) | 斜率測驗(3)
  • 6. Quiz on Slope (2) | 斜率測驗(2)
  • 7. Quiz on Slope (1) | 斜率測驗(1)
  • 8. Quiz on Gradient of Line (1)
  • 9. Quiz on Gradient : Calculation of gradient
  • 10. Gradient of Line Self Quiz
  • 11. ACCESS - Slope Exercises

3.1.

Gradient (Slope): Intuitive Introduction

[color=#000000]Discovery Lesson Activity: [br][/color][b][color=#0000ff][url=https://docs.google.com/document/d/1s6Y3t5X_LWgMsiGgOxYvakgmC_mq3chrkGEV1oaji9I/edit?usp=sharing.]Gradient(Slope): Intuitive Introduction Investigation [br][br][/url][/color][/b]Original lesson by Tim Brezinski [br] [url=https://www.geogebra.org/material/show/id/Xutr9rPj]https://www.geogebra.org/material/show/id/Xutr9rPj[/url][br]Modified to use the word gradient instead of slope for local students
– Lew W. S., Tim Brzezinski

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3.10.

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3.11.

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4.

Functions in Gradient Intercept form y = mx + c

  • 1. Relating a Linear Graph to its equation(function) in gradient and intercept form
  • 2. Gradient and Y Intercept of Straight Line & its Equation
  • 3. Steps in Finding Equation of Straight Lines 求直線方程的步驟
  • 4. Self Review on gradient and y intercept for y = mx + c, ax + by = c, ax + by + c = 0
  • 5. Reading Slopes from Equation of Straight Lines 由直線方程讀取斜率
  • 6. Gradient Intercept Form of Equation of line (linear function)
  • 7. Exploring the linear graph of y = m x + c
  • 8. 4Q Quiz: Graphing Linear Equations; Identifying Slope & y-intercept (With Hints)
  • 9. Graphing Linear Equations; Identifying Slope & y-intercept (With Hints)
  • 10. Graphing a Given Linear Equation (Self Practice)
  • 11. Linear (Straight Line) Graphs - Different forms of equation
  • 12. Equation of a Straight Line Given Linear Graph (Practice)

4.1.

Relating a Linear Graph to its equation(function) in gradient and intercept form

[size=150][size=200]Drag the [color=#0000ff][b]blue[/b][/color] and [color=#ff0000][b]red[/b][/color] [b]points[/b] on the graph and see how the equation of the graph is related to the graph.[br](Use mouse scroll wheel to zoom in or out, and drag screen to pan view of graphic screen.)[br][/size][/size]
[size=200]Q1 In the equation [i][b]y[/b][/i] = [i][color=#6aa84f][b]m[/b][/color][b]x[/b][/i] + [color=#ff0000][b]c [br][/b][/color][/size][br][size=200] what does [i][b][color=#38761d]m[/color][/b][/i] represent ?[/size]
[size=200]Q2 In the equation [i][b]y[/b][/i] = [i][color=#6aa84f][b]m[/b][/color][b]x[/b][/i] + [color=#ff0000][b]c [br][/b][/color][/size][br][size=200] what does [i][b][color=#ff0000]c[/color][/b][/i] represent ?[/size]
[size=200]Q3 [br]For the graph of function [i][b]y[/b][/i] = [color=#6aa84f][b][i]-[/i]4[/b][/color][b]x[/b] + [color=#ff0000][b]5 [br][/b][/color][/size][br][size=200] what is the gradient of the line graphed?[/size]
[size=200]Q4 [br]For the graph of function [i][b]y[/b][/i] = [color=#6aa84f][b][i]-[/i]4[/b][/color][b]x[/b] + [color=#ff0000][b]5 [br][/b][/color][/size][br][size=200] what is the value of [i]y [/i]where the line intersects[br] the [i]y[/i] axis?[/size]
– Lew W. S.

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4.12.

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5.

Application of linear graphs in real world contexts

  • 1. Distance Time Graph ( in metres and seconds)
  • 2. Temperature Graph with Thermometer Display
  • 3. Linear Function Contextual Problems : Cost of T Shirts
  • 4. Linear Function Contextual Problems : Cost of Printing Cards

5.1.

Distance Time Graph ( in metres and seconds)

Visualize the Distance Time Graph (Self Directed Learning)
Use the ShowViewScaleControls checkbox to display other controls for adjusting the distance time graph for any problem you wish to understand and solve
– Lew W. S.

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Information