[Maths Class Notes] on Line Graph Pdf for Exam

Line Graph Definition:

Line graphs are used to represent the mutual variation of any two quantities that are either directly or inversely proportional to each other. For example, the prices for different materials of cloth are different. The price of the cloth increases with the increase in the quality and durability of the cloth. Silk clothes are costlier than cotton clothes. So, this kind of direct variation can be represented in the form of lines using line graphs. If all the lines in various types of line graph are straight lines, then the graph is called a rectilinear graph or simply linear graph. 

Parts of Line Graph:

There are several terms that are associated with the parts of a line graph. A few important terms associated with line graphs are:

1. Coordinate Axes: The horizontal and vertical lines that intersect each other and are mutually perpendicular to each other. These axes are generally labelled as XX’ and YY’. The two quantities that are proportional to each other are represented by certain values on the coordinate axes.

2. Origin: The point of intersection of both the coordinate axes is called the origin. It is represented by the letter O. At this point, the values of both the variable quantities is zero.

3. Title: Every line graph has a title at the top of the graph. It gives a brief idea of the quantities being represented.

4. Scale: While representing the data which large amounts the measurements are scaled to a lower value by a scaling factor to fit the graph into the size of the paper. This is called scaling. The scale of the line graph definition is generally represented at the top right corner of the paper. 

Types of Line Graphs: 

There are different types of line graphs that are classified based on number of lines and nature of lines with respect to the coordinate axes. 

Based on the number of lines, line graphs are classified as:

1. Single Line Graphs 

The line graphs are the graphs that consist of only one single line that represents the variation of two quantities. 

Example: The variation of work and time in a line graph can be represented in the form of a single line. This is because the amount of work decreases linearly with the time available. This instance is one of the uses of line graphs.

2. Double Line Graphs

The graphs that consist of two lines representing the same data variation at two different cases are called the double line graphs.

Example: The average rainfall during different months in a year for two different cities can be represented by a double line graph. Each line in this graph corresponds to the average rainfall in one city.

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3. Compound Line Graphs

These graphs represent the variation of any two quantities in many different cases. It consists of more than 3 lines. Each line corresponds to the variation of the quantities in different systems.

Based on the nature of lines with respect to the coordinate axes, the different types of line graphs are:

1. Straight Line Graphs:

The line graphs in which the variation of any two quantities is represented by a straight line are called straight line graphs or linear graphs and the line graphs indicating the variation with curved lines are called curvilinear graphs. 

2. Horizontal Line Graphs:

The line representing the variation is parallel to the X axis and perpendicular to the Y axis. This kind of graph indicates the variation of quantity represented on X axis when the quantity on Y axis does not change.

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3. Vertical Line Graphs:

The graphs in which the line indicating the variation is parallel to the Y axis and perpendicular to the X axis. It indicates that the quantity on X axis is constant when the quantity on Y axis is varying. 

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To understand the steps to construct a line graph, let us take an example of the table below which indicates the daily earning of a person on weekdays. 

How to Make a Line Graph:

Step 1: 

Construct the coordinate axes X and Y which are the important parts of line graph. Represent the days of the week on X axis and the Earnings in the increments of 100 on Y axis.

Step 2:

Plot the points of earnings on the graph against the corresponding values of X axis.

Step 3:

Join the points that are plotted on the graph using a rule or free hand.

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Fun Quiz:

1. Recall what is a line graph and observe the figure below and identify which of the given statements are true.

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1. (A) indicates decrease in current with time

2. (B) indicates the increase in current with time

3. (C) indicates that the current is independent of time

4. (E) indicates that the current decreases linearly with time

2. The graphs in which the direct and inverse variations are represented in the form of straight lines is 

1. Bar graph 

2. Curved graph

3. Linear graph