Introduction to Graphs
Class 8 · Mathematics
4 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Reading a Line Graph
A line graph shows how something changes over time. Time goes along the horizontal axis and the measurement goes up the vertical axis. Each reading is a point, and the points are joined by straight lines. Going up means the value rises and going down means it falls. A point between two readings can be estimated from the line.
Why it matters. Graphs appear in newspapers, health charts and school reports. Reading them correctly helps children spot trends and compare numbers quickly.
Try it in two minutes
- Ask your child to note the outdoor temperature at 9 a.m., 12 noon and 3 p.m. on a sunny day.
- Draw the axes on squared paper, mark the times along the bottom and temperatures up the side.
- Plot the three points and join them.
- Ask: when was it hottest? When did the temperature rise fastest? What might it have been at 10 a.m.?
Try at home. Track the weight of a plant or the height of a family member each week for a month and ask your child to draw a line graph.
Reading a Distance-Time Graph
In a distance-time graph, time is on the horizontal axis and distance from the start is on the vertical axis. The distance covered in one hour is the difference between two readings. A flat line means the object did not move, and a steeper line means a faster speed.
Why it matters. Travel timetables, fitness trackers and many science experiments use these graphs. Children should learn to read changes, not just single values.
Try it in two minutes
- Say a story: you walked 2 km in the first hour, 3 km in the second, rested for the third hour, and then walked 2 km.
- Ask your child to make a table of the total distance at the end of each hour.
- Draw the graph on squared paper and join the points.
- Ask: which part of the line is flat? Which part is steepest?
Try at home. Time a short walk around the house or park and note the distance every minute, then draw a graph of it.
Plotting Points and Choosing Scales
To draw a graph, first choose which quantity goes on each axis: the quantity we choose (independent) goes on the horizontal axis and the one that depends on it goes on the vertical axis. Choose a scale, such as 1 square for 10 rupees. Then plot each pair as (horizontal value, vertical value) and join the points.
Why it matters. Drawing graphs turns tables of numbers into pictures that are easier to understand. Wrong scales or swapped coordinates are the most common mistakes.
Try it in two minutes
- Ask your child to make a table of 1, 2, 3 and 4 pencils against their cost at ₹ 6 each.
- On squared paper, draw the two axes and choose a scale that fits the largest value.
- Plot each pair, writing the number of pencils first.
- Join the points and ask: what shape did you get? Does it pass through the corner where the axes meet?
Try at home. Make a table of the number of laps and the time taken on a short run, and draw the graph with a scale you choose.
Linear Graphs and Direct Variation
When two quantities vary directly, such as the cost and the number of articles at a fixed price, their graph is a straight line through the origin. We can use the line to find values that are not in the table: find the value on one axis, go straight to the line, then across to the other axis.
Why it matters. Estimating from a graph is useful for prices, interest and travel plans. It also shows children why direct proportion is linked to straight lines.
Try it in two minutes
- Make a table: 1 kg costs ₹ 40, 2 kg cost ₹ 80, 3 kg cost ₹ 120. Ask your child to plot the points.
- Join the points. Ask: does the line pass through the corner where the axes meet? Why?
- Ask: what does the line say about the cost of 2.5 kg?
- Use the line to find how many kg can be bought for ₹ 100.
Try at home. Choose a price list in a shop, draw the cost against weight and use the line to answer two questions.
What your child will practise
- Linear Graphs and Direct Variation: Jungle Quick Fire (Quick Fire)
- Plotting Points and Choosing Scales: Candy Puzzle (Clue Puzzle)
- Plotting Points and Choosing Scales: Candy Quick Fire (Quick Fire)
- Reading a Distance-Time Graph: Mission Control Quest (Collect the Answer)
- Reading a Line Graph: Number Quest (Collect the Answer)
- Quiz: Linear Graphs and Direct Variation (8 questions)
- Quiz: Plotting Points and Choosing Scales (8 questions)
- Quiz: Reading a Distance-Time Graph (8 questions)
- Quiz: Reading a Line Graph (8 questions)