Introduction to Graphs Exercise 15.1 — Class 8 NCERT Solutions & Concepts

Welcome to the world of visual mathematics! In CBSE Class 8 Maths, Chapter 15 introduces us to the powerful tool of graphs. Specifically, the focus of the introduction to graphs ex 15 1 class 8 ncert exercises is all about learning how to read, interpret, and analyze line graphs. A line graph displays data that changes continuously over periods of time, helping us spot trends at a glance. Whether you are tracking a patient's fever over several hours or a company's annual sales over five years, graphs make numerical data incredibly easy to digest.

In this guide, our YoLearn AI Tutor will walk you through the core concepts of Exercise 15.1. You will master how to read horizontal and vertical axes, understand scales, identify trends, and accurately answer data-extraction questions. By the end of this page, you will be solving Ex 15.1 questions effortlessly and with absolute precision! Let's get started on your sketchpad.

What is a Line Graph and Why Do We Use It?

Data in the form of raw numbers can be hard to interpret quickly. For instance, if you have a list of a patient's body temperature recorded every hour, comparing those numbers to see when the fever peaked takes time. A line graph solves this by plotting these data points on a grid and connecting them with straight line segments. The horizontal line is called the x-axis, which usually represents independent quantities like time, hours, or years. The vertical line is the y-axis, representing dependent quantities like temperature, distance, or sales. Together, they create a visual path. If the line goes up, the value is increasing; if it goes down, the value is decreasing. This visual trend analysis is the heart of CBSE Class 8 Maths Exercise 15.1.

Step-by-Step Guide to Reading a Line Graph

  1. Identify the Axes — Look at the horizontal axis (x-axis) and the vertical axis (y-axis) to see what variables they represent and what units of measurement are used (e.g., time in hours, temperature in °C).
  2. Understand the Scale — Determine what each small division on the grid lines represents. For example, if 1 major grid division on the y-axis represents 5 units, each smaller grid mark might represent 1 unit.
  3. Locate the Point — Find the specific position on the graph for the given query. For instance, if asked about the temperature at 1:00 PM, locate '1:00 PM' on the x-axis and look straight up to find the plotted point.
  4. Read the Value — From that plotted point, move horizontally to the left to meet the y-axis. The value on the y-axis is your answer.

Worked Examples from Exercise 15.1 Concepts

  • Example 1: A graph shows a company's sales (in Lakhs of Rupees) over four years. In 2018, sales were ₹4 Lakhs, and in 2019, they were ₹8 Lakhs. Find: (i) The increase in sales from 2018 to 2019. (ii) The average sales for these two years. Step-by-step Solution: Step 1: Write down the sales value for 2018 = ₹4 Lakhs. Step 2: Write down the sales value for 2019 = ₹8 Lakhs. Step 3: To find the increase, subtract the 2018 value from the 2019 value: ₹8 Lakhs - ₹4 Lakhs = ₹4 Lakhs. Step 4: To find the average sales, add both values and divide by 2: (₹4 Lakhs + ₹8 Lakhs) / 2 = ₹12 Lakhs / 2 = ₹6 Lakhs.
  • Example 2: A patient's temperature chart shows temperatures at different times of the day. At 10:00 AM, the temperature was 37.5°C and at 11:00 AM, it was 39.0°C. During which period did the temperature rise the most if the temperature at 12:00 Noon was 38.5°C? Step-by-step Solution: Step 1: Check change between 10:00 AM and 11:00 AM: 39.0°C - 37.5°C = 1.5°C rise. Step 2: Check change between 11:00 AM and 12:00 Noon: 38.5°C - 39.0°C = -0.5°C (decrease of 0.5°C). Step 3: Comparing the two periods, the temperature rose the most between 10:00 AM and 11:00 AM with a rise of 1.5°C.

Exam Tips to Avoid Common Mistakes

When solving introduction to graphs ex 15 1 class 8 ncert problems, students often make errors in reading the scale. Always pay close attention to the scale of the vertical axis! If the interval between 36 and 37 has 10 small lines, each small line represents 0.1 units. If there are only 2 small lines, each represents 0.5 units. Another common mistake is confusing the coordinates—always read the x-axis first (horizontal line) and then the y-axis (vertical line).

Practice Questions with Solutions

  • Q: A company's sales in different years are as follows: 2015: ₹5 Crores, 2016: ₹8 Crores, 2017: ₹8 Crores, 2018: ₹12 Crores. (a) What were the sales in 2016 and 2018? (b) Compute the difference between sales in 2015 and 2018. A: Step 1: Identify the values from the given data: Sales in 2016 = ₹8 Crores. Sales in 2018 = ₹12 Crores. Step 2: For part (b), subtract the sales of 2015 from the sales of 2018. Step 3: Difference = Sales in 2018 - Sales in 2015 = ₹12 Crores - ₹5 Crores = ₹7 Crores. Final answer: (a) Sales in 2016 was ₹8 Crores, and in 2018 was ₹12 Crores. (b) The difference is ₹7 Crores.
  • Q: In an experiment in biology, two different plants, Plant A and Plant B, were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. At the end of Week 1: Plant A = 2 cm, Plant B = 2 cm; Week 2: Plant A = 7 cm, Plant B = 9 cm; Week 3: Plant A = 9 cm, Plant B = 10 cm. (a) How high was Plant A after 2 weeks? (b) How much did Plant B grow from the end of Week 2 to the end of Week 3? A: Step 1: From the recorded values, locate the height of Plant A at the end of Week 2. It is 7 cm. Step 2: For part (b), identify the height of Plant B at the end of Week 2 (9 cm) and Week 3 (10 cm). Step 3: Subtract the height at Week 2 from the height at Week 3: 10 cm - 9 cm = 1 cm. Final answer: (a) Plant A was 7 cm high after 2 weeks. (b) Plant B grew by 1 cm.
  • Q: A patient's temperature was recorded at hourly intervals. At 1:00 PM, it was 36.5°C, and at 2:00 PM, it was also 36.5°C. What was the temperature of the patient at 1:30 PM? Explain how you arrived at your conclusion using graph-reading concepts. A: Step 1: On the x-axis, find the point midway between 1:00 PM and 2:00 PM, which corresponds to 1:30 PM. Step 2: Observe the line joining the points for 1:00 PM and 2:00 PM. Since the temperature is the same (36.5°C) at both 1:00 PM and 2:00 PM, the line graph segment is completely horizontal (flat) between these times. Step 3: A flat horizontal line means the temperature remained constant during this entire hour. Final answer: The temperature at 1:30 PM was 36.5°C because the graph segment remains flat and constant.
  • Q: A motorist travels from a town to a nearby city. The distance traveled at different times is: 8:00 AM: 0 km, 9:00 AM: 30 km, 10:00 AM: 40 km, 11:00 AM: 80 km. (a) How far did the motorist travel between 9:00 AM and 11:00 AM? (b) During which hour-long interval did they travel the maximum distance? A: Step 1: Find the distance at 9:00 AM (30 km) and 11:00 AM (80 km). Step 2: Subtract to find the distance traveled: 80 km - 30 km = 50 km. Step 3: Calculate the distance covered in each 1-hour interval: - 8:00 AM to 9:00 AM: 30 km - 0 km = 30 km - 9:00 AM to 10:00 AM: 40 km - 30 km = 10 km - 10:00 AM to 11:00 AM: 80 km - 40 km = 40 km. Step 4: Compare these values: 40 km is the highest value, which occurred between 10:00 AM and 11:00 AM. Final answer: (a) The motorist traveled 50 km. (b) The maximum distance was traveled between 10:00 AM and 11:00 AM.

Frequently Asked Questions

What is the main purpose of a line graph?

A line graph visualizes how numerical values change continuously over a specific period of time. This makes it easy to identify trends, such as growth rates or temperature changes, at a single glance.

What does a completely horizontal line segment mean on a line graph?

A horizontal line segment indicates that there is no change in the value of the dependent variable over that time interval. The value remains constant.

How do we choose the scale for a line graph?

We choose a scale by looking at the minimum and maximum values of our data. The scale should fit all data points clearly on the grid without squeezing them too closely together or leaving too much blank space.