Class 8 Mathematics Chapter 13 Introduction To Graphs

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I. Chapter Summary:

This chapter introduces students to the concept and utility of graphs in representing data visually. It covers various types of graphs—bar graphs, pie charts, line graphs, and linear graphs. Students learn to plot points on the Cartesian plane using coordinates, interpret graph-based data, and use linear graphs to represent equations in two variables. The chapter forms a crucial base for statistics, algebra, and real-life data analysis in higher classes.

II. Key Concepts Covered:

III. Important Questions

(A) Multiple Choice Questions (1 Mark)

1. The coordinates of a point lying on the y-axis are:
   a) (x, x)
   b) (0, y)
   c) (x, 0)
   d) (0, 0)
   Answer: b) (0, y)

2. (PYQ 2020) A line graph is useful when we want to show:
   a) Shapes
   b) Trends over time
   c) Angles
   d) Pie representation
   Answer: b) Trends over time

3. Which point lies on the x-axis?
   a) (0, 4)
   b) (3, 0)
   c) (2, 2)
   d) (1, 5)
   Answer: b) (3, 0)

4. The horizontal axis in a Cartesian plane is called:
   a) Y-axis
   b) Z-axis
   c) X-axis
   d) Graph line
   Answer: c) X-axis

(B) Short Answer Questions (2/3 Marks)

1. Plot the following points on a graph: A(2, 3), B(4, 1), C(0, 0).

2. From the given bar graph (provide a figure in actual test), answer: Which item had the highest quantity sold?

3. (PYQ 2019) Interpret the temperature graph of a city and mention which day was the coldest.

4. Write the coordinates of the point lying at the intersection of x = 5 and y = 2.

(C) Long Answer Questions (5 Marks)

1. Draw a line graph showing the population of a town over five years. Use hypothetical data.

2. Plot and label the points A(1, 2), B(2, 3), C(3, 4), D(4, 5). What do you observe about the points?

3. (PYQ 2018) Study the rainfall line graph for five months and answer:
   a) In which month was rainfall maximum?
   b) Which months saw a decrease in rainfall?

4. Create a bar graph from the following data:
   Fruits Sold in a Day – Apples: 20, Bananas: 35, Mangoes: 15, Oranges: 30.

(D) HOTS – Higher Order Thinking Skills

1. A student plots the points A(2, 3), B(3, 4), C(4, 5), and finds they lie on a straight line. Can you derive an equation relating x and y from these points?

2. The sales of ice creams increase steadily from January to May. What type of graph is most appropriate to represent this trend? Create such a graph using made-up data.

IV. Key Formulas / Concepts

V. Deleted Portions (CBSE 2025–2026):

No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026):

VII. Previous Year Questions (PYQs)

VIII. Real-World Application Examples

• Weather Forecasting: Interpreting temperature or rainfall line graphs.

• Health Charts: Tracking height/weight/BMI trends using line graphs.

• Business & Sales: Representing profits or product sales via bar/line graphs.

• Transportation: Distance-time graphs for vehicles.

• Mobile Apps/Data Usage: Graphical representation of internet/data usage over time.

IX. Student Tips & Strategies for Success (Class 8 Specific)

Time Management:

• Dedicate 15 minutes weekly to reading and plotting data from newspapers or apps.

• Use real datasets (sports scores, school attendance) for practice.

Exam Preparation:

• Practice plotting both points and graphs.

• Revise concepts of quadrants and coordinates.

• Use graph paper to avoid careless plotting errors.

Stress Management:

• Use colors or stickers to make graphs more visually engaging.

• Relate graph questions to personal interests (e.g., cricket stats, marks trend).

X. Career Guidance & Exploration

 For Classes 9–10:

• Builds base for Statistics, Algebra, and Coordinate Geometry.

• Required for NTSE, Olympiads, and math aptitude tests.

For Classes 11–12:

• Critical in:

  • Data Science

  • Economics

  • Engineering

  • Environmental Science

  • Market Analysis

• Relevant exams: JEE (Coordinate Geometry), CUET (Data Interpretation), NDA (Graph Reading)

XI. Important Notes

• Label axes clearly and always mention scale.

• Plot points accurately using graph paper.

• Choose the appropriate graph type based on the nature of data.

• Practise interpreting from both given and self-made graphs.