Introduction to Graphs | Class 8 Mathematics Notes
By ConceptScroll Team · Published on 17 July 2026 · 5 min read
Introduction to Graphs – this guide gives you a concise, exam-ready overview of Introduction to Graphs from Class 8 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.
13.1 Introduction
Graphs are an essential tool in mathematics and everyday life for representing numerical data visually. They allow us to see patterns, trends, and comparisons quickly and clearly, which might be difficult to discern from raw data or tables alone. This section introduces the concept of graphs as visual representations of data collected from various sources such as newspapers, television, magazines, and books. The primary purpose of a graph is to present numerical facts in a form that can be easily understood and analyzed. Although data can be presented in tabular form, graphs are particularly useful when showing changes over time or comparing different sets of data. One common type of graph is the line graph, which displays data that changes continuously over time. For example, a doctor may record a patient's body temperature every few hours and represent this data on a time-temperature graph. In such a graph, the horizontal axis (called the x-axis) typically represents time intervals, while the vertical axis (called the y-axis) represents the measured values, such as temperature. Plotting points corresponding to each time and temperature pair and then connecting these points with line segments results in a line graph. This visual representation helps identify patterns, such as increases or decreases in temperature over time, and can even suggest values at times when no measurements were taken by observing the trend of the graph. The section also briefly recalls that graphs can be used to represent various types of data and sets the stage for more detailed study of graphing techniques and interpretations in subsequent sections.
📊 Diagram: Fig 13.1 Each piece of data is shown by a point on the square grid.; Fig 13.2 The points are then connected by line segments. The result is the line graph.
🧪 Activity: Observe a time-temperature graph and identify the pattern of temperature changes over the day.
🔗 Connection: This introduction leads to examples of interpreting line graphs and understanding the information conveyed by the axes and plotted points.
Frequently asked questions
1. The following graph shows the temperature of a patient in a hospital, recorded every hour. (a) What was the patient’s temperature at 1 p.m.? (b) When was the patient’s temperature 38.5°C? (c) The patient’s temperature was the same two times during the period given. What were these two times? (d) What was the temperature at 1.30 p.m.? How did you arrive at your answer? (e) During which periods did the patients’ temperature showed an upward trend?
Solution: (a) From the graph, the temperature at 1 p.m. is 38°C.
(b) The temperature was 38.5°C at 12 noon and 3 p.m.
(c) The temperature was the same at 12 noon and 3 p.m. (38.5°C).
(d) At 1.30 p.m., the temperature is between 38°C (at 1 p.m.) and 38.5°C (at 2 p.m.). By interpolation, it is approximately 38.25°C.
(e) The temperature showed an upward trend from 11 a.m. to 12 noon and from 2 p.m. to 3 p.m.
2. The following line graph shows the yearly sales figures for a manufacturing company. (a) What were the sales in (i) 2002 (ii) 2006? (b) What were the sales in (i) 2003 (ii) 2005? (c) Compute the difference between the sales in 2002 and 2006. (d) In which year was there the greatest difference between the sales as compared to its previous year?
Solution: (a)(i) Sales in 2002 = 20,000 units (from graph) (a)(ii) Sales in 2006 = 40,000 units
(b)(i) Sales in 2003 = 25,000 units (b)(ii) Sales in 2005 = 35,000 units
(c) Difference between sales in 2002 and 2006 = 40,000 - 20,000 = 20,000 units
(d) The greatest difference compared to previous year is between 2005 and 2006 (40,000 - 35,000 = 5,000 units).
3. For an experiment in Botany, 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. The results are shown by the following graph. (a) How high was Plant A after (i) 2 weeks (ii) 3 weeks? (b) How high was Plant B after (i) 2 weeks (ii) 3 weeks? (c) How much did Plant A grow during the 3rd week? (d) How much did Plant B grow from the end of the 2nd week to the end of the 3rd week? (e) During which week did Plant A grow most? (f) During which week did Plant B grow least? (g) Were the two plants of the same height during any week shown here? Specify.
Solution: (a)(i) Plant A after 2 weeks = 15 cm (a)(ii) Plant A after 3 weeks = 20 cm
(b)(i) Plant B after 2 weeks = 10 cm (b)(ii) Plant B after 3 weeks = 15 cm
(c) Growth of Plant A during 3rd week = 20 cm - 15 cm = 5 cm
(d) Growth of Plant B from 2nd to 3rd week = 15 cm - 10 cm = 5 cm
(e) Plant A grew most during the 3rd week (5 cm growth)
(f) Plant B grew least during the 1st week (growth less than other weeks)
(g) Both plants were of the same height at the start (week 0) and possibly at
4. The following graph shows the temperature forecast and the actual temperature for each day of a week. (a) On which days was the forecast temperature the same as the actual temperature? (b) What was the maximum forecast temperature during the week? (c) What was the minimum actual temperature during the week? (d) On which day did the actual temperature differ the most from the forecast temperature?
Solution: (a) Days when forecast temperature = actual temperature are Tuesday and Friday.
(b) Maximum forecast temperature during the week = 38°C (on Sunday).
(c) Minimum actual temperature during the week = 30°C (on Wednesday).
(d) The actual temperature differed most from forecast on Thursday.
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