Definition, Examples | What Is Linear Graph? - Cuemath

Linear Graph

Linear graph is represented in the form of a straight line. To show a relationship between two or more quantities we use a graphical form of representation. If the graph of any relation gives a single straight line then it is known as a linear graph. The word "linear" stands for a straight line. The linear graph is a straight line graph that is drawn on a plane connecting the points plotted on x and y coordinates.

1.	Linear Graph Definition
2.	Linear Graph vs Line Graph
3.	Linear Graph Equation
4.	FAQs on Linear Graph

Linear Graph Definition

"A linear graph is the graphical representation of a straight line." It showcases a linear equation in two variables and shows the linear association between two quantities.

Let's understand with the help of an example.

James was offered a job where he would be paid $15 per hour. He has an average daily expenditure of $50. He wants to know, how many minimum hours he should work in a day so that he has some savings. Let's study how a linear graph can answer this problem.

If we represent time by t and income by I, we get a linear equation: I =15t

With the help of the above plotted linear graph, we can analyze that the value on the vertical axis is more than his expenditure of $50.

The value on the horizontal axis gives the minimum number of hours James should work to have some savings every day.

According to the graph if he will work 5 hours daily then he can manage his earnings up to $ 75($15 × 5 hours = $ 75) and he can have savings $(75 - 50) of $ 25.

Linear Graph vs Line Graph

Let's understand the difference between a linear graph and a line graph with help of an image.

In the figure given above, can you make out how B is different from A?

Here, A is a linear graph whereas B represents a line graph.

Though both of them are made up of line segments, there is a major difference between them.

The difference lies in the figure obtained after joining the line segments. All the points in a linear graph are collinear and hence lie on a line.

But in the case of a line graph, they may or may not be collinear.

Linear Graph Equation

A linear graph is the graphical representation of a linear equation.

A linear equation is an equation that can be written in the form: Ax + By = C, for some real numbers A, B, and C where A and B, are not 0.

For example, the linear equation 2x + 5y = 0 on a graph looks like this:

How To Plot Linear Equation On a Graph?

Consider the following steps to plot a linear equation on a graph:

• step1: Identify the two quantities which are varying.
• step2: Let the 1st quantity be x and the 2nd quantity is y.
• step3: Next, find out three ordered pairs (x, y) which satisfy the given equation.
• step4: Present these values in a tabular form.
• step5: Plot the points given in the table on a cartesian plane.
• step6: Join the points.

For example, 2x + y = 6

To plot this on a graph we write it in the form y = mx + b

So, y =−2x + 6

To get the solution to the linear equation, we can plug in a numerical value to x and obtain the corresponding value for it.

Three of the solutions are:

x	0	1	-1
y	6	4	8

Now, plot these points on an XY plane and join them.

Important Notes:

• To plot a linear graph, two pairs of (x,y) are sufficient. But, we won't come to know if there is a mistake in obtaining these values as two points can always be joined and they represent a line. It is advised to plot one more point to ensure that the solutions obtained for the given linear equation are correct.
• The equation y = kx (where k is a real number) represents a line parallel to X-axis i.e. horizontal line.
• The equation x = ky (where k is a real number) represents a line parallel to Y-axis i.e. vertical line.

☛ Related Articles

Check out these interesting articles to know more about the linear graph and its related topics.

• Line Graphs
• Introduction To Graphing
• Graphing Linear Equations