Complete Guide For Class 8th Math Chapter 15 Introduction To Graphs

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The chapter “Introduction to Graphs” of class 8 in mathematics introduces students to graphs, a visual representation of data. Key topics include the Cartesian plane, plotting points, interpreting line graphs, bar graphs, and pie charts. Students learn how to analyze and interpret data trends, making graphs a vital tool in mathematics and real-life applications.

Introduction to Graphs

In mathematics, a graph is a collection of points and lines connecting some subset of them. The points, known as vertices or nodes, are connected by lines, referred to as edges, arcs, or simply lines. Graphs are essential tools for representing data visually, making it easier to understand relationships and trends.

Types of Graphs

In the chapter “Introduction to Graphs”, we will now learn the types of graphs.

1. Bar Graphs A bar graph displays comparisons among categories using parallel vertical or horizontal bars. Each bar represents a category and its corresponding value, making it easy to compare data across different groups.
   Example: A Bar Graph
2. Pie Graphs (Circle Graphs) A pie graph is a circular chart divided into sectors, each representing a proportion of the whole. It is used to compare parts of a whole, with each sector proportional to the quantity it represents.
   Example: Pie Graphs
3. Histograms A histogram is a type of bar graph that shows data in intervals. Unlike standard bar graphs, histograms have adjacent bars with no gaps between them, representing continuous data ranges.
   Example: Histograms
4. Line Graphs Line graphs are used to display data that changes continuously over time. They consist of points connected by line segments, illustrating trends or patterns in the data.
   Example: Time-Temperature Line Graph

Linear Graphs

Linear graphs are a specific type of line graph where the data points form a straight line. These graphs represent linear relationships, where the rate of change between variables is constant. To draw a linear graph, one must locate points on a graph sheet using coordinates.

Co-ordinates

Coordinates are used to specify the position of a point on a graph. They are given as pairs of numbers, representing the horizontal (x-axis) and vertical (y-axis) positions, respectively.

Dependent & Independent Variables

In graphing, variables are classified into two types: dependent and independent.

• Independent Variables: These are variables that are manipulated to observe their effect on dependent variables. They are usually plotted on the x-axis.
• Dependent Variables: These are the variables that change in response to the independent variables. They are usually plotted on the y-axis.

Example: Consider the following data showing the speeds of different objects:

This data can be represented using a bar graph, with the objects on the x-axis and their corresponding speeds on the y-axis.

Another example involves representing the market position of different tea brands using a pie chart:

The pie chart visually illustrates the market share of each brand, with each sector’s size proportional to the percentage of buyers.

Graphs are fundamental tools in mathematics and various real-life applications. They allow us to visualize data, identify patterns, and make informed decisions based on trends. This chapter equips students with the skills to interpret and create various types of graphs, enhancing their analytical abilities.