Introduction to Graphs

Graphs present numerical information visually so that patterns and trends can be seen at a glance. In this chapter you will revise bar graphs, pie charts and histograms, and then study line graphs, which show how a quantity such as the temperature of a patient or the sales of a shop changes over time. You will learn how to read a line graph, find the highest and lowest values and identify periods of increase or decrease. You will also meet linear graphs, line graphs that are a single straight line. To draw graphs accurately you need coordinates. You will learn about the x-axis, the y-axis and the origin (0, 0), and see that each point is described by an ordered pair (x, y), so (4, 6) and (6, 4) are different points. Finally, you will draw graphs for relations such as distance and time at a constant speed, simple interest and principal, and perimeter and side of a square, identifying the independent and dependent variables.

Detailed Worksheet: Introduction to Graphs Section A - Definitions (10 marks) 1. What is a line graph? Give two situations in which a line graph is the best way to show data. (2 marks) 2. What is a linear graph? Give one example of a relation that gives a linear graph. (2 marks) 3. What are the coordinates of a point? In the point (4, 3), name the x-coordinate and the y-coordinate and explain what each tells us. (2 marks) 4. What is the origin? Write the coordinates of any point on the x-axis and any point on the y-axis. (2 marks) 5. What are independent and dependent variables? Identify them in a graph of distance travelled against time. (2 marks) Section B - Calculations and Applications (15 marks) 6. Consider the points P(0, 3), Q(4, 0), R(2, 5) and O(0, 0). (i) Which point lies on the x-axis? (ii) Which lies on the y-axis? (iii) Write the coordinates of the point that is 3 units to the right of the origin and 2 units up. (3 marks) 7. A car travels at a uniform speed of 40 km/h. Write the distance covered after 1, 2, 3 and 4 hours as ordered pairs (time, distance). How long will the car take to travel 100 km? (3 marks) 8. The simple interest for one year at 10% per annum on a principal of Rs 100, Rs 200, Rs 300, Rs 500 and Rs 1,000 is to be shown on a graph. Write the ordered pairs (principal, interest). What principal gives an interest of Rs 35 in one year? (3 marks) 9. A patient's temperature was recorded as: 6 am 37.0 degrees C, 8 am 37.8 degrees C, 10 am 38.5 degrees C, 12 noon 38.2 degrees C, 2 pm 37.6 degrees C, 4 pm 37.0 degrees C. (i) What was the highest temperature and when? (ii) During which period was the temperature rising? (iii) By how much did it fall from 10 am to 4 pm? (3 marks) 10. Write the perimeter and the area of a square of side 2, 3, 4 and 5 cm. Which of the two, perimeter or area, will give a linear graph when plotted against the side? Give a reason. (3 marks) Section C - Diagrams (10 marks) 11. Plot the points (2, 3), (5, 3), (5, 7) and (2, 7) on a graph sheet and join them in order. Name the figure formed and find its perimeter and area. (4 marks) 12. Plot the points (1, 2), (2, 4), (3, 6) and (4, 8). Do they lie on a straight line? Does the line pass through the origin? From the graph, find y when x = 2.5. (3 marks) 13. Draw a line graph for the temperature data given in Question 9, using a suitable scale on each axis. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Ajit cycles from his home to a market and back. His distance from home was 0 km at 8:00 am, 5 km at 8:30 am, 10 km at 9:00 am, 10 km at 9:30 am and 0 km at 10:00 am. Draw the distance-time graph. (i) How long did he stay at the market? (ii) What was his speed while going and while returning? (iii) On which part of the journey was he faster? (iv) What total distance did he cycle? (5 marks) 15. Decide which of these relations give a linear graph, with reasons: (i) perimeter and side of a square (ii) area and side of a square (iii) cost and number of notebooks at a fixed price (iv) simple interest and time for a fixed principal and rate. Plot the values for (ii) for sides 1 to 4 cm to show the shape of its graph. (5 marks) 16. Shop P sells apples at Rs 50 per kg. Shop Q sells them at Rs 40 per kg but charges Rs 50 for home delivery. Write the cost at each shop for 1 to 6 kg and draw both graphs on the same axes. For what quantity are the costs equal, and which shop is cheaper for larger quantities? Which graph passes through the origin? (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Draw every graph on graph paper, label both axes, give each graph a title and state the scale used.