Why do we need Graphs?
Graphs are used to pictorially represent data relationships. It is a simple way to show data values that are too large or complex to be fully conveyed in the text and in a small amount of space. Now, let us look at the most commonly used graph – line graphs.
What are Line Graphs?
A line graph is a type of chart or graph that is used to display data that varies over time. A line graph can be created by connecting several points using straight lines. The x-axis, which is the horizontal axis, and the y-axis, which is the vertical axis, are the two axes of a line graph. The x-axis is usually the time period axis.
It is possible to compare two variables by plotting multiple lines on the same axis. However, when there are too many lines plotted on the same graph, it becomes cluttered and difficult to read.
How do we Analyze Graphs?
Here are the steps to follow to make an analysis of a graph.
- Check the title.
- Observe how the axes are labeled.
- To understand the trend, observe the pattern of variation in data values.
- To obtain precise figures, look at the data values.
Solved Examples
Example 1:
Does the graph below represent a linear function? Explain.
Solution:
No. As we can see the graph is not a straight line.
Hence, it does not represent a linear function.
Example 2:
Jane earns $10 per hour and Jack earns $7 per hour. The functions m = 10h and m = 7h show the relationship between the number of hours(h) they work and the money(m) they earn. Plot a line graph and find which graph is steeper? Explain.
Solution:
Let’s plot the graph using the given data.
From the graph, we see the graph with m = 10h is steeper.
The reason it is steeper is because Jane’s hourly earnings are greater than Jack’s hourly earnings.
Hence, the line graph for m = 10h is steeper.
Example 3:
Simon has made a line graph of the number of cheesecakes he sold each week during a certain duration of time. Based on the information provided in the graph, find the decrease in the number of cheesecakes sold in week 8 compared to week 7.
Solution:
From the graph, we can say that,
Number of cheesecakes sold in week 7 = 90
Number of cheesecakes sold in week 8 = 10
So, the difference = 90 – 10
= 80
Therefore, there was a decrease of 80 cheesecakes sold in week 8 when compared to week 7.
In the real-world, graphs are used in many scenarios like sales, maps, social media, web page search volumes, city planning, traffic control, and in many other instances.
There are different types of graphs such as bar charts, line graphs, pie charts and pictographs.
A pie chart is a type of graph in which a circle is divided into sectors with each sector representing a percentage of the whole.
A bar graph is a pictorial representation of data using rectangular bars of equal width and varying height or length. The height or length of the bars are used to represent the numerical values of variables.