RS Aggarwal Class 8 Mathematics Solutions for Chapter-23 Line Graphs and Linear Graphs

What is a Line Graph?

It is a type of graph that displays the continuous data that is changing over some time. It is made by joining the series of data points using a line segment consecutively.

What is a Linear Graph?

It is a straight line graph drawn on a plane that connects points on the x and y-axis. A linear graph represents the linear relationship between two variables.

Line graphs are of three types:

• Single Line graph

• Double line graph

• Compound line graph

Steps to Construct a Line Graph

• On a graph draw two lines parallel to each other. The x-axis is the horizontal line and the y-axis is the vertical line.

• Choose an appropriate scale along the x-axis.

• Make the points.

• Join each point with the consecutive point using a ruler. Thus, a line graph is obtained.

• Example of a line graph:

(image will be uploaded soon)

How to Interpret a Line Graph?

You can interpret line graphs by studying the data and analysing it. Interpreting the line graph data is:

• Making sense of the given data.

• Answering queries using the given data.

• Making predictions based on the trends.

• Finding the value of one variable given the value of the other and so on.

For Example:

Question: The line graph given below shows the yearly sales figures for a manufacturing company during the last five years.

(image will be uploaded soon)

Question. Study the graph given above and answer the following questions given below:

(i) Compute the sales in,

(a) 2013

(b) 2015

(c) 2016?

(ii) Compute the reduction between sales in 2012 and 2016?

(iii) Find out the year in which there was the greatest difference between the sales as compared to the previous year?

Solution:

(i) The sales in

(a) 2013 was Rs 7 cr.

(b) 2015 was Rs10 cr.

(c) 2016 was Rs 8 cr.

(ii) after computing the reduction between sales in 2012 and 2016 is Rs 4 cr.

(iii) The greatest difference was in 2015.

Single Line Graphs

A graph used to show changes over time is called a Line graph. A line graph consisting of a single line is known as a single line graph. The single line graph is used to represent only a single data set.

Example of a single line graph:

(image will be uploaded soon)

Double Line Graphs

A line graph with two lines connecting points to show a continuous change is called a Double line graph. As shown before in a line graph, the lines can ascend and descend in a double line graph.

A double line graph has two axes. In the graph, the occurrences and categories being compared over time are represented by the x-axis, and the scale is represented by the y-axis. A set of numbers representing the data which is organised into equal intervals is called a scale.

Example of Double line graph:

(image will be uploaded soon)

What is a Cartesian Plane?

• A plane in which two perpendicular axes intersect each other is known as the cartesian plane.

• The x-axis and the y-axes are the horizontal axes and the vertical axis respectively.

• The point at which both the axes intersect is known as the origin and is denoted by O.

• Both the axis, that is, the x-axis and the y-axis are known as the coordinate axis.

• The x-coordinate is located at a given distance from the y-axis and the y-coordinate is located at a given distance from the x-axis at a point denoted by P. 

• The abscissa and the ordinates are the names given to the x-coordinate and the y-coordinate respectively.

Introduction to Linear Graph

It is a collection of points that can form a straight line. The graph (straight line) that is formed while representing the relationship between the x-axis and the y-axis is called a linear graph.

For fixing a point on the graph sheet you need, x-coordinate and y-coordinate.

Class 8 Maths Chapter 23 - Line Graphs and Linear Graphs: At A Glance

• The two coordinates, that is, abscissa and ordinates represent data pictorially in the cartesian plane.

• The graphs show the relation between two types of quantities or objects.

• Graphs are of various types such as line graph, linear graph, bar graph, pie chart, and histogram.

• The two types of graphs described in this chapter are line graphs and linear graphs.

• If you represent the data on the x-y plane in the form of straight unbroken lines, it is known as a linear graph.

• When the data is represented on the x-y plane in the form of straight lines or curves, it is known as a line graph.

• Independent variables are the ones whose value does not change with respect to the value of another quantity. Independent variables are also known as control variables.

• Dependent variables are those variables whose value changes with respect to another quantity. 

Uses of Line Graphs:

• In order to track changes over a short and long period of time, line graphs are used.

• In order to compare the changes for different groups over the same period of time,  line graphs are used.

• It is the best graph to represent data whenever small changes in data exist.

Examples of line graphs:

Some real-life examples of line graphs are:

• Line graphs help in describing future contract markets and opportunities.

• Line graphs are also constructed by the pharmaceutical sector to determine the accurate strength of drugs.

• Line graphs are also used by the government for the preparation of the budget.

• Line graphs are also used to estimate if an individual's body weight is according to their height.

Preparation Tips

• First, go through the chapter thoroughly and cover all the topics.

• Note down all the important formulae and try to learn them.

• Start solving the exercise questions without any guidance from anyone.

• Try the questions at least 3 times if you are unable to solve them.

• Seek help from Vedantu’s solution to check your answers and solve the ones that you were unable to solve.