NCERT Solutions for Class 8 Maths Chapter 13 Introduction to Graphs

What is a Graph in Mathematics?

A graph is a visual representation of data shown in a numerical form. It helps us understand the relationship between two or more quantities quickly. Instead of looking at a long, boring table of numbers, a graph allows you to see trends, such as whether a value is increasing, decreasing, or staying the same over time.

In your introduction to graphs class 8 maths question answer sets, you will work with several important types:

• Bar Graph: This uses bars of uniform width to compare different categories. The height of each bar represents its value. It is best used when comparing values.

• Pie Chart: Also called a circle graph, this shows the relationship of parts to a whole.

• Histogram: A special type of bar graph that shows data in continuous intervals.

• Line Graph: This displays data that changes continuously over periods of time using points joined by line segments.

• Linear Graph: A line graph that consists of a single unbroken straight line and shows a constant rate of change.

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Introduction to Graphs Class 8 NCERT Solutions

Exercise 13.1 – Reading Graphs

1. A patient's temperature in a hospital was recorded every hour. What was the patient’s temperature at 1 p.m. based on the graph?
   Sol: First, find 1 p.m. on the horizontal x-axis. Move vertically up to the graph line. From that point, move horizontally to the y-axis. The value lies between 36 and 37.
   Ans: 36.5 degrees Celsius.

2. At what time was the patient’s temperature 38.5 degrees Celsius?
   Sol: Locate 38.5 on the y-axis. Move horizontally to the graph line, then move down to the x-axis.
   Ans: 12 noon.

3. The patient’s temperature was the same during two specific periods. Which were these?
   Sol: Look for a flat (horizontal) section of the graph. This shows no change in temperature.
   Ans: 1 p.m. to 2 p.m.

4. During which period did the temperature increase the fastest?
   Sol: Identify the steepest upward part of the graph. That indicates the fastest increase.
   Ans: Between 10 a.m. and 11 a.m.

5. When was the temperature the lowest?
   Sol: Locate the lowest point on the graph and match it to the time on the x-axis.
   Ans: Early morning (as per graph).

6. What was the temperature at 3 p.m.?
   Sol: Find 3 p.m. on the x-axis, move up to the graph, then across to the y-axis.
   Ans: 37°C (approx).

7. Between which two times did the temperature fall?
   Sol: Look for the downward sloping part of the graph.
   Ans: Between 12 noon and 1 p.m.

Read More - NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Exercise 13.2 – Plotting Graphs

8. Sales of a company in 2002 were 4 crores and in 2006 were 8 crores. Plot these as points.
   Sol: Mark years on the x-axis and sales on the y-axis. Plot (2002, 4) and (2006, 8).
   Ans: Points are (2002, 4) and (2006, 8).

9. Plot the following points on a graph sheet: A(4, 0), B(4, 2), C(4, 6), D(4, 2.5). Do they lie on a line?
   Sol: All points have x = 4, so they lie vertically on the same line.
   Ans: Yes, they lie on a straight line.

10. Draw a graph for side of a square and its perimeter: (2,8), (3,12), (5,20).
    Sol: Plot the points and join them. The points form a straight line.
    Ans: Linear graph.

11. Plot (1,1), (2,2), (3,3), (4,4). Does the line pass through origin?
    Sol: Plot all points and extend the line backwards.
    Ans: Yes, it passes through (0,0).

12. A car travels distances 30, 60, 90, 120 km at 7, 8, 9, 10 a.m. How much distance between 7:30 and 8 a.m.?
    Sol: From graph, distance at 7:30 is 45 km and at 8 is 60 km. Difference = 15 km.
    Ans: 15 km.

13. Interest on ₹1000 is ₹80 annually. Find interest on ₹2500 using graph.
    Sol: Plot (1000,80), (2000,160), extend the line. Read value at 2500.
    Ans: 200.

14. Plot points (2,4), (4,8), (6,12). Are they collinear?
    Sol: Plot all points. They lie on a straight line.
    Ans: Yes, collinear.

15. Plot (0,5), (1,5), (2,5). What type of line is formed?
    Sol: All y-values are the same, forming a horizontal line.
    Ans: Horizontal line.

16. Plot (3,0), (3,2), (3,5). What do you observe?
    Sol: All x-values are the same, so points lie vertically.
    Ans: Vertical line.

17. Plot (2,3), (3,5), (4,7). Is the graph linear?
    Sol: Plot and join the points. They form a straight line.
    Ans: Yes, linear graph.

18. Plot (1,2), (2,4), (3,9). What do you observe?
    Sol: The points do not lie on a straight line.
    Ans: Non-linear graph.

Read More - NCERT Solutions for Class 8 Civics Chapter 5 – Judiciary

Long answers for Chapter 13 Graphs

What are Cartesian Plane and Coordinates in Graphs?

A graph is built using two lines. The horizontal line is the x-axis, and the vertical line is the y-axis. These lines meet at a point called the origin, written as (0, 0).

Every point is written as (x, y).

• The first value shows movement along the x-axis

• The second value shows movement along the y-axis

Getting this order right is important. A small mistake here can shift your entire graph and affect your introduction to graphs class 8 question answer

What are the Steps to Draw a Graph?

The steps to draw a graph are :

• Draw two perpendicular lines for the x-axis and y-axis

• Mark the origin (0, 0) clearly

• Choose a suitable scale based on the data

• Label both axes properly

• Plot each coordinate carefully

• Join the points neatly using a ruler (if required)

Following these steps keeps your graph neat, readable, and accurate for any introduction to graphs class 8 question answer.

 How to Check Your Graphing Results

• Check your scale before plotting

• Ensure axes are not swapped

• Use a ruler for straight lines

• Make sure the trend makes logical sense

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