CBSE Class 8 Maths: Introduction to Graphs - Exercise 15.2

Understanding the Graph Sheet and Coordinates

A graph sheet, also known as a Cartesian plane or coordinate plane, is your canvas for plotting data. It's formed by two perpendicular lines: the horizontal X-axis and the vertical Y-axis. These axes intersect at a point called the origin, which has coordinates (0,0). Every point on this plane can be uniquely identified by an ordered pair of numbers, (x, y), where 'x' is the value on the X-axis (also called the abscissa) and 'y' is the value on the Y-axis (the ordinate). When plotting, the first number in the pair tells you how far to move horizontally from the origin, and the second number tells you how far to move vertically. Remember, positive x values move right, negative x values move left. Positive y values move up, and negative y values move down. For Class 8, we often focus on the first quadrant where both x and y are positive. Choosing an appropriate scale for your axes is crucial so that your graph is clear and all data points fit.

Step-by-Step: Plotting Points and Interpreting Graphs

1. Step 1: Prepare Your Graph Sheet — Draw the X-axis (horizontal) and Y-axis (vertical) on your graph paper. Mark the origin (0,0) where they meet. Decide on a suitable scale for each axis. For example, '1 unit = 1 cm' or '1 unit = 5 items'. This scale helps represent large numbers effectively and clearly.
2. Step 2: Plotting an Ordered Pair (x, y) — To plot a point like (3, 5): 1. Start at the origin (0,0). 2. Move along the X-axis to the value 'x' (3 units to the right for positive 3). 3. From that position, move parallel to the Y-axis to the value 'y' (5 units up for positive 5). 4. Mark this spot with a dot and label it (e.g., Point A). This point (3, 5) represents 3 units on the X-axis and 5 units on the Y-axis.
3. Step 3: Reading Coordinates from a Plotted Point — If a point (say, Point P) is already plotted on the graph: 1. Draw a perpendicular line from Point P to the X-axis. The value where it touches the X-axis is the x-coordinate. 2. Draw another perpendicular line from Point P to the Y-axis. The value where it touches the Y-axis is the y-coordinate. 3. Write the coordinates as an ordered pair (x, y). For example, if it touches 4 on X and 6 on Y, the coordinates are (4, 6).
4. Step 4: Interpreting Data from a Graph — Once points are plotted and possibly connected to form a line or curve, you can answer questions about the relationship shown. For example, if a graph shows 'Time vs. Temperature': 1. To find temperature at a specific time: Locate the time on the X-axis, go up to the graph line, then move horizontally to the Y-axis to read the temperature. 2. To find the time when temperature was specific value: Locate the temperature on the Y-axis, go across to the graph line, then move vertically down to the X-axis to read the time.

Exam Tip: Avoiding Common Graphing Mistakes

Graphing can be tricky, but knowing common pitfalls can help you ace it! A frequent mistake is not labeling axes properly. Always write what each axis represents (e.g., "Time (in hours)", "Distance (in km)") and include units. Another error is choosing an inconsistent or unsuitable scale. Ensure your scale is uniform (e.g., each big square represents 10 units, not 10 units for one square and 5 units for another). Also, make sure all your data points fit on the graph without being cramped. Finally, remember the order of coordinates: it's always (x, y), not (y, x). Plotting (5, 3) instead of (3, 5) is a common oversight that leads to incorrect results.

Practice Questions with Solutions

• Q: Plot the following points on a graph sheet: A(2, 4), B(5, 1), C(0, 3). A: Step 1: Draw the X and Y axes, marking the origin (0,0). Choose a scale, e.g., 1 unit = 1 cm. Step 2: For A(2, 4), move 2 units right on X-axis, then 4 units up on Y-axis. Mark and label 'A'. Step 3: For B(5, 1), move 5 units right on X-axis, then 1 unit up on Y-axis. Mark and label 'B'. Step 4: For C(0, 3), stay at 0 on X-axis, then move 3 units up on Y-axis. Mark and label 'C'. Final answer: Points A, B, and C are correctly plotted on the graph sheet.
• Q: A graph shows the quantity of milk (in litres) consumed by a family over 5 days. If the points are (1, 2), (2, 2.5), (3, 3), (4, 2.5), (5, 2.5). What was the maximum milk consumed and on which day? A: Step 1: Examine the y-coordinates (quantity of milk) of all given points: 2, 2.5, 3, 2.5, 2.5. Step 2: Identify the largest y-coordinate, which is 3. Step 3: Find the x-coordinate (day) corresponding to this maximum y-coordinate. The point is (3, 3), so the day is 3. Final answer: The maximum milk consumed was 3 litres, and it was consumed on Day 3.
• Q: Write the coordinates of the point where the X-axis and Y-axis intersect. A: Step 1: Recall the definition of the origin in a Cartesian plane. Step 2: The point where the X-axis and Y-axis intersect is called the origin. Step 3: The coordinates of the origin are always (0, 0). Final answer: The coordinates are (0, 0).
• Q: Observe a linear graph showing distance covered (Y-axis in km) versus time taken (X-axis in hours). If a point (2, 80) is on the graph, what does it signify? A: Step 1: Understand that the x-coordinate represents time and the y-coordinate represents distance. Step 2: For the point (2, 80), the x-value is 2 hours and the y-value is 80 km. Step 3: Combine these interpretations. Final answer: The point (2, 80) signifies that a distance of 80 km was covered in 2 hours.

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