Introduction to Graphs | Class 8 Mathematics Notes
By ConceptScroll Team · Published on 17 July 2026 · 4 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.
13.2 Some Applications
This section explores practical applications of graphs in everyday life, focusing on relationships between dependent and independent variables. It explains that in many real-world scenarios, one quantity depends on another; for example, the amount of electricity consumed (independent variable) affects the electricity bill amount (dependent variable). Such relationships can be effectively represented using graphs. The section introduces the concepts of independent (control) variables and dependent variables, emphasizing that the independent variable is the one we choose or control, while the dependent variable changes in response. A real-life example is given where the number of litres of petrol purchased determines the total cost to be paid. The quantity of petrol is the independent variable, and the cost is the dependent variable. By plotting such data on a graph, one can visualize the direct relationship between the two quantities. This understanding is foundational for analyzing linear relationships and direct variation in subsequent examples.
📊 Diagram: Fig 13.5
🧪 Activity: Think and discuss which variable is independent when buying petrol and paying the bill.
🔗 Connection: This section leads into examples of plotting graphs to show direct variation and interpreting them.
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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