Class 8 Math Introduction to Graphs Notes

Introduction to Graphs – Class 8

Hi everyone! This chapter introduces Graphs. Graphs are a visual way to represent information or data, making it easier to understand trends and relationships.

What are Graphs?

A graph is a diagram that shows the relationship between two or more sets of data. We often use a coordinate plane, which has two axes: the x-axis (horizontal) and the y-axis (vertical).

Coordinate Plane

Coordinates:

Points on the graph are represented by coordinates (x, y). The x-coordinate tells you how far to move horizontally, and the y-coordinate tells you how far to move vertically.

Example: The point (2, 3) is located 2 units to the right on the x-axis and 3 units up on the y-axis.

Types of Graphs

There are different types of graphs, each suited for different kinds of data:

1. Bar Graphs:

Use bars of different lengths to represent data values. Good for comparing different categories.

Example: A bar graph can show the number of students in each grade of a school.

2. Line Graphs:

Use lines to connect data points, showing trends over time. Good for showing changes.

Example: A line graph can show the change in temperature over a day.

3. Pie Charts:

A circle divided into sections, where each section represents a proportion of the whole. Good for showing parts of a whole.

Example: A pie chart can show the percentage of different types of books in a library.

4. Histograms:

Similar to bar graphs, but used for continuous data (data that can take any value within a range). The bars touch each other.

Example: A histogram can show the distribution of heights of students in a class.

Plotting Points on a Graph

To plot a point (x, y) on a graph:

Start at the origin (0, 0).
Move x units horizontally along the x-axis (to the right if x is positive, to the left if x is negative).
Move y units vertically along the y-axis (up if y is positive, down if y is negative).
Place a dot at that location.

Applications of Graphs

1. Science:

Showing experimental results, analyzing data.

2. Business:

Tracking sales, visualizing market trends.

3. Geography:

Representing population data, showing geographical distributions.

4. Everyday Life:

Tracking personal finances, understanding statistics in the news.

Graphs are powerful tools for communicating information clearly and effectively.

Introduction to Graphs Quiz – Tough Application Problems

1. **Distance-Time Graph:** A car travels at varying speeds. The distance it covers is plotted against time. If the graph shows a steeper slope at one point, what does that indicate about the car’s speed at that time?

The car’s speed is higher at that time.

A steeper slope on a distance-time graph indicates a greater change in distance over a given time interval, which means a higher speed.

2. **Temperature Change:** A line graph shows the temperature change over 24 hours. If the graph shows a sharp peak, followed by a gradual decline, what could this represent?

A sudden increase in temperature, followed by a gradual cooling down.

A peak represents a high point in temperature, and a decline shows temperature decreasing. This could be due to factors like the sun rising and then setting.

3. **Sales Data:** A company’s sales figures for different quarters are represented in a bar graph. If one bar is significantly shorter than the others, what could this indicate?

Lower sales for that particular quarter.

The length of the bar represents the sales figures. A shorter bar means lower sales compared to other quarters.

4. **Population Distribution:** A pie chart represents the population distribution of different age groups in a city. If one slice of the pie is much larger than the others, what does this signify?

That age group represents a larger proportion of the city’s population.

The size of the slice is proportional to the percentage of the population it represents. A larger slice means a larger population share.

5. **Analyzing Trends:** A line graph shows the growth of a plant over several weeks. If the line is relatively flat for the first few weeks and then starts to rise sharply, what does this suggest about the plant’s growth pattern?

The plant’s growth was slow initially, but then accelerated significantly.

A flat line indicates little to no growth, while a rising line indicates growth. The sharp rise suggests a period of rapid growth.

6. **Interpreting Coordinates:** On a graph, point A is located at (3, -2) and point B is located at (-1, 4). Which point is further to the right on the graph?

Point A

The x-coordinate determines how far to the right (positive) or left (negative) a point is. 3 is greater than -1, so Point A is further to the right.

7. **Graphing a Relationship:** The cost of renting a bicycle is Rs. 50 per hour. Create a table of values showing the cost for 1, 2, 3, and 4 hours. Then, plot these points on a graph with time on the x-axis and cost on the y-axis. What kind of graph do you get?

A straight line graph.

The relationship between time and cost is directly proportional (cost = 50 * time). This will result in a straight line when plotted on a graph.

8. **Real-World Data:** Imagine you are tracking the amount of rainfall in your city each month. What type of graph would be most suitable to represent this data and why?

A line graph or a bar graph.

Both line graphs and bar graphs would be suitable. A line graph would effectively show the trend of rainfall over time, while a bar graph would make it easy to compare the amount of rainfall in different months.

9. **Combined Analysis:** A graph shows both the number of hours studied and the scores achieved by students on a test. If the graph shows an upward trend, what does this suggest about the relationship between study time and test scores?

More study time tends to be associated with higher test scores.

An upward trend indicates a positive correlation. As one variable (study time) increases, the other variable (test scores) also tends to increase.

10. **Interpreting Changes:** A line graph shows the stock price of a company over several months. If the line shows a sudden drop at one point, followed by a gradual rise, what could this indicate?

A significant event (e.g., a negative news announcement) that caused the stock price to fall, followed by a recovery in the stock price.

A sharp drop indicates a sudden decrease in value, while a gradual rise suggests recovery or growth. This could be due to various market factors or company-specific news.