Definition Types and How to Plot Graphs with Examples
Significance of Introduction to Graphs
The mathematics chapter of Introduction to Graphs helps you understand and study the graphical representation of data. The various arrangements of data for the purpose of comparison, analysis, or representation are made using these graphs.
You will be able to learn this Introduction to Graphs Class 8 chapter quickly with the help of our notes. Go through them attentively and make sure you familiarise yourself with the nuances of this chapter. This will eventually help in your academics and understanding or representing a large set of data using graphs.
Introduction to Graphs in Maths
To elaborate this concept, here large volume of numerical data is represented in graphical or pictorial format for the ease of understanding. A graph can have multiple applications such as the comparison between categories, observing the change over a period, data in short intervals, etc.
For any of the applications, the Introduction of Graph Theory discusses several kinds of methods or graphical or pictorial representation of data. A few of them are mentioned below.
Bar graphs
As discussed in Class 8 Introduction to Graphs, bar graphs use bars of an identical width to represent the proportion of various quantities or categories. It is widely used for comparison.
Below represents a bar graph which shows profits earned by a company in different years.
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Bar graphs can also be used to indicate more than one type of data and then compare and analyse them. An introduction to graph theory west chapter also discusses double bar graphs. Refer to the image below to understand double bar graphs. It represents the maximum temperature rise in four different seasons in two different years (1950 and 2000).
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Histograms
As per NCERT Class 8 Introduction to Graphs, histograms are similar to bar graphs even though they are a continuous representation of data. Here, the data is grouped in regular intervals but continuous forms. For instance, the histogram shown below represents the distribution or frequency of people in a city as per their age.
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Pie Charts
In Class 8 Maths Introduction to Graphs, a pie graph is described as a circular representation of the entire data. It is used for cases when a few portions of a whole needs to be represented.
For instance, this pie chart indicates what percentage of people like to watch which genre movie. From the pie chart, it is clear that 30% of people like to watch movies from the romantic genre.
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Linear and Line Graphs
A line graph is the one where data points vary with the change in time. And as per NCERT Class 8 Maths Introduction to Graphs chapter, linear graphs are the one wherein all the points draw into a straight line.
For instance, observing the change in data over a period can be best observed with a line graph, as shown below.
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Further, a linear graph has data which forms into a straight line and has two variables in the two axes.
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Since you are familiar with CBSE Class 8 Maths Introduction to Graphs concepts, you will be able to solve the exercise questions with ease. For more comprehensive learning, you can download our Vedantu app and start learning. The study notes and Introduction to Graphs Class 8 questions prepared meticulously by our expert tutors will surely help you clear exams with flying colours.
FAQs on Introduction to Graphs in Mathematics
1. What is a graph in mathematics?
A graph in mathematics is a visual representation of the relationship between two variables on a coordinate plane. In coordinate geometry, a graph shows how one variable (usually y) changes with another variable (usually x).
- A graph is drawn on the Cartesian plane.
- Each point on the graph is written as an ordered pair (x, y).
- Graphs can represent linear equations, quadratic functions, inequalities, and real-life data.
2. What are the parts of a graph?
The main parts of a graph are the x-axis, y-axis, origin, and plotted points. These components form the coordinate system used in graphing.
- X-axis: Horizontal axis.
- Y-axis: Vertical axis.
- Origin: The point (0, 0) where both axes meet.
- Quadrants: Four regions formed by the axes.
- Scale: The units marked on each axis.
3. What is the Cartesian coordinate system?
The Cartesian coordinate system is a two-dimensional plane formed by perpendicular x-axis and y-axis used to locate points using ordered pairs. Each point is written as (x, y), where:
- x represents horizontal distance from the origin.
- y represents vertical distance from the origin.
4. How do you plot a point on a graph?
To plot a point on a graph, move along the x-axis first and then move vertically according to the y-value. Follow these steps:
- Start at the origin (0, 0).
- Move horizontally to the x-value.
- Move vertically to the y-value.
- Mark the point.
5. What is a linear graph?
A linear graph is a straight-line graph that represents a linear equation of the form y = mx + c. Here:
- m is the slope (gradient).
- c is the y-intercept.
6. What is the slope of a graph?
The slope of a graph measures the steepness of a line and is calculated as m = (y₂ − y₁) / (x₂ − x₁). It shows how much y changes for a change in x.
- If m > 0, the line rises.
- If m < 0, the line falls.
- If m = 0, the line is horizontal.
7. What is the difference between a bar graph and a line graph?
The main difference is that a bar graph compares categories using bars, while a line graph shows trends over time using connected points.
- Bar graph: Uses rectangular bars to represent discrete data.
- Line graph: Uses points joined by lines to show continuous data.
8. How do you draw the graph of a linear equation?
To draw the graph of a linear equation, find at least two solutions and join them with a straight line. Steps:
- Write the equation, e.g., y = x + 2.
- Choose values for x (e.g., 0 and 2).
- Find corresponding y-values (2 and 4).
- Plot points (0,2) and (2,4).
- Join the points with a straight line.
9. What are quadrants in a graph?
The quadrants are the four regions of the Cartesian plane divided by the x-axis and y-axis. They are labeled counterclockwise:
- Quadrant I: (+, +)
- Quadrant II: (−, +)
- Quadrant III: (−, −)
- Quadrant IV: (+, −)
10. Why are graphs important in mathematics?
Graphs are important because they visually represent mathematical relationships and make data easier to interpret. In mathematics and data analysis, graphs help to:
- Understand relationships between variables.
- Identify trends and patterns.
- Compare quantities clearly.
- Solve equations graphically.
