2.5 Linear models

  2. Functions
  3. 2.5 Linear models
    4. 30'

Straight line functions

Commonly seen in the form y = f(x) = mx + c where m represents the gradient/rate of change of the function and c is the y-intercept, where x = 0. These models are a fundamental bit of algebra that come up again and again. they are also fairly commonly used models. For example an electricity bill often has a standing charge that you pay even before you have used any electricity (this is the y - intercept, because amount of electricity used, x = 0) and then a given amount for every unit of electricity used (this is the gradient of the cost graph - it goes up by this amount for every unit of electricity used)

Key Concepts

In this unit you should learn to…

  • Understand the general expression of a linear function \(y=mx+c\) with gradient and y-intercept

  • Understand that linear functions model situations where there is a constant rate of change

  • Derive and use linear models

 

Essentials

Slides Gallery

Use these slides to review the material and key points covered in the videos.

 

1. Linear Functions

This video is about the nature of linear relationships and how they appear as plotted functions on a coordinates grid.

 

2. Plotting linear functions

This video goes through the process of plotting linear functions from the equations.

 

3. Fractional Gradients

This video covers linear functions with fractional gradients

 

4. Negative gradients

This video covers linear functions with negative gradients

 

Examples

This video looks at lots of examples of linear functions

 

Other Forms

What happens when the function/relation is not shown as y = mx + c?

 

Finding values

This video looks at a linear function in context finding the value of one of the variables when you know the other.

 

Summary

This section of the page can be used for quick review. The flashcards help you go over key points and the quiz lets you practice answering questions on this subtopic.

Review these condensed 'key point' flashcards to help you check and keep ideas fresh in your mind.

 

Test yourself

Self Checking Quiz

Practice your understanding on these quiz questions. Check your answers when you are done and read the hints where you got stuck. If you find there are still some gaps in your understanding then go back to the videos and slides above.

 

 

Exam Style Questions

The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.

Question 1

Video solution

 

Question 2

Video solution

Question 3

Video solution: Coming Soon

MY PROGRESS

How much of 2.5 Linear models have you understood?