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Math Lesson 14.1.1 - What are Linear Graphs
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Welcome to our Math lesson on What are Linear Graphs, this is the first lesson of our suite of math lessons covering the topic of Linear Graphs, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
What are Linear Graphs?
In the previous chapters, we dealt with many situations involving linear graphs. We have seen that linear graphs occur when there is a linear relationship between two variables: the independent one (usually denoted by x) and the dependent one (usually denoted by y). The term "linear" refers to a straight line.
To be more precise, we must emphasize the fact that linear graphs only have meaning in coordinate systems. These systems must be at least two-dimensional in order to contain at least two variables, where one of them is called independent (it is called so because the values of this variable are given by the user, who is independent in his/her decision on which values to consider). The other variable depends on the values of the independent variable and the formula that gives the relationship between the two variables (hence the name 'dependent'). All combinations between these two variables give a line in the X-Y system, which may be straight or not, depending on the type of relation between the variables involved.
By definition, a linear graph is the graphical representation of a straight line.
In other words, a linear graph is an illustration of a first-order equation with two variables, where the coordinates of each point of the graph make the equation true when substituted into the equation. For example, the figure below shows the linear graph 2x + y = 5 and all the three points A, B and C, which are part of the graph (the first coordinate indicates the value of x and the second coordinate that of y), make the equation 2x + y = 5 true when substituting these coordinates in it.
Let's prove the above sentence. Thus, substituting the coordinates of point A(0, 5) in the equation 2x + y = 5 yields
5 = 5 (true)
When substituting the coordinates of point B(1, 3) we obtain
2 + 3 = 55 = 5 (true)
and when substituting the coordinates of point C(2, 1) in the equation, yields
4 + 1 = 5
5 = 5 (true)
More Linear Graphs Lessons and Learning Resources
Whats next?
Enjoy the "What are Linear Graphs" math lesson? People who liked the "Linear Graphs lesson found the following resources useful:
- Definition Feedback. Helps other - Leave a rating for this definition (see below)
- Linear Graphs Math tutorial: Linear Graphs. Read the Linear Graphs math tutorial and build your math knowledge of Linear Graphs
- Linear Graphs Revision Notes: Linear Graphs. Print the notes so you can revise the key points covered in the math tutorial for Linear Graphs
- Linear Graphs Practice Questions: Linear Graphs. Test and improve your knowledge of Linear Graphs with example questins and answers
- Check your calculations for Linear Graphs questions with our excellent Linear Graphs calculators which contain full equations and calculations clearly displayed line by line. See the Linear Graphs Calculators by iCalculator™ below.
- Continuing learning linear graphs - read our next math tutorial: Slopes and Gradients
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