Before You Watch

This video shows you how to interpret a linear equation and graph it on a Cartesian plane. So, it will refresh your memory of how to use a Cartesian plane and develop your understanding of what the graph of a linear equation means.

This topic also builds on the fundamental concepts of algebra covered in Introduction to Algebra. So, if you're unsure about algebra in general, watch that video first, then come back.

The Video

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Some Practice Questions

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Now What?

Linear equations are widely used to model situations, so they are an important category of graph to understand. Once you're comfortable graphing linear functions, then it’s a good idea to look at how you can interpret word problems and create a linear equation from the description. Some lessons on how to do this can be found here:

https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebra-linear-equation-word-problems/v/linear-equation-word-problem-example

More example questions are available here:

https://www.ixl.com/math/algebra-1/solve-linear-equations-word-problems

 

When you're confident with creating, graphing and solving linear equations, the next logical step is to look at situations where two (or more) linear equations are used together to find a solution. This is shown in Simultaneous Equations.

But When I am Going to Use This

Linear equations are very commonly used in everyday life to model situations, so you will run into them a lot. Some simple examples of applications of linear functions include:

  • costing a phone call or taxi ride
  • calculating revenue and expenses for a company against items sold
  • doubling or halving a recipe for cooking
  • feeding a group of people at a party
  • working out driving time against distance to travel.

 

Other Links

Maths is Fun has a lot of useful applets and summaries for a wide variety of mathematics subjects. One applet that is particularly relevant for this topic is their equation grapher. You can enter a mathematical equation (in terms of x and y, so if your letters are different, just change them to x and y) and it will graph that equation. Keep in mind, however, you will still need to be able to graph them with pen and paper yourself!

Fort Bend Tutoring has a series of YouTube videos covering numerous different mathematical concepts. This specific video covers graphing a linear equation by finding the x and y intercepts (a method very similar to what we did here).

The Khan Academy has a comprehensive set of video tutorials covering a large range of mathematical and other concepts, as well as questions to test your knowledge. The first link below is to an entire chapter dedicated to linear equations. It includes lots of videos, examples and quizzes. The second link leads to a demonstration of how to interpret a word problem in terms of a linear equation.

Patrick JMT (Just Maths Tutorials) has a comprehensive set of video tutorials covering a large range of mathematical concepts. This content shows how to graph a linear equation using two different methods: finding the x and y intercepts (similar to what we did here), and the point and slope method.