Introduction to Graphs

Pie Charts and Linear Graphs

Have you noticed that all the slices of the pizza are equally cut? Every slice is an equal part of the whole pizza. Cutting out a piece of cake or a pie also forms some sectors of the circle. Similarly, you can depict some useful information in the form of a sector of a circle. This can be done by making Pie Charts. The Pie Chart is a collection of slices showing the numerical proportion. Let’s see how to make a chart and a linear graph in this section.

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Pie Charts

A pie chart is a circular representation of data. In it, data is represented by sector of a circle. The sectors of the circle are like the slices of a pie or pizza. The only difference is that in a pie chart the sectors are of different sizes. The size of each sector is related to its frequency. Let’s see how to make a chart.

Properties of Pie Charts

  • The total angle of a circle is 360°.
  • Each sector of the circle shows various observations of the data.
  • The whole circle represents the sum of the values of the observation.
  • The angle of the particular sector is calculated as ((Value of the component) / Total value) × 360°.
  • If the data is in percentage form, the angle of the sector becomes ((Percentage value of component) / 100) × 360°. It shows the percentage distribution of the observations.

How to Make a Chart?

  1. Draw a circle of any radius.
  2. Calculate the angles of each sector by the above formula.
  3. Draw the various sectors.
  4. Color each sector of your choice.

The pie chart below shows the proportion of the number of employees on the basis of their qualification.

make a chart

Linear Graphs

Just like a line graph, a linear graph is formed when a set of coordinates are joined by a set of a line segment. The only difference is that these line segments are so joined that they form an unbroken line. In other words, we will have a straight line when all the set of points join. Let us get familiar with the term co-ordinates.


Suppose you are blindfolded and one of your friends is giving you directions to move. If he says move 5 steps to the right and then 5 steps in front. What will you do? You first go right or move front first? If you are saying right then you are a good listener. But if you are going to move in front you are wrong.

Maybe he asked you to move right first because maybe after some steps there is a pillar or some obstruction. Finding the coordinates of a point is just like this. Below is the graph showing the coordinates (3, 5).

make a chart

Construction of Linear Graph

  1. Draw two lines perpendicular to each other.
  2. The horizontal line forms the x-axis and the vertical is the y-axis.
  3. The coordinates are the ordered pair of the numbers. The first number represents the x-axis and the later one is the y-coordinate.
  4. Join the various set of points.

It is linear as we always get a straight line when we plot the points on a graph. Suppose Mr. X is walking in a park. He starts to count his footsteps and the distance covered. As distance increases, the number of footsteps also increases and vice-versa. Below is a graph showing the linear relationship between the number of footsteps and the distance covered.

Pie Charts

It is interesting to know that we can sometimes predict some future value based on the pattern of the linear graph.

Solved Examples for You

Question 1: Are the coordinates (4, 5) and (5, 4) the same? Why?

Answer : No, (4, 5) and (5, 4) are not the same. In (4, 5) the x-coordinate is 4 whereas in (5, 4) it is 5. The same is with the y-coordinate too. As a result, they are different and they represent the different sets of points.

Question 2: Draw the following points on the graph and answer the following questions.

(2, 210), (5, 420), (7, 560), (6, 490), (3, 280), (1, 140), (8, 630)

  1. Is it a linear graph?
  2. What is the value of x-coordinate if y-coordinate corresponds to 350?
  3. If the graph is linear, find the value of y-coordinate for which x-coordinate is 11.

Solution: The graph for the above points.

Pie Charts

  1. The graph is a linear graph.
  2. The coordinates of the point will be (4, 350).
  3. The value will be 840. The coordinates of the point will be (11, 840).

This concludes our discussion on how to make a chart and a linear graph.

Question 3: What is the meaning of the pie chart in mathematics?

Answer: A Pie Chart, also known as a pie graph is a chart that uses the ‘pie slices’ to represent the relative sizes of data. This chart is divided into various segments, where each sector displays the relative size of every single value.

Question 4: Does a linear graph have to be straight?

Answer: Every linear equation forms straight lines when graphed. However, all linear equations don’t form linear functions. For being a linear function, a graph needs to be both linear and a function.

Question 5: Is a pie chart a graph?

Answer: Yes, a pie chart is a spherical graph that represents the relative contribution that is contributed by various categories to an overall total. A wedge of the sphere symbolizes the contribution of each category.

Question 6: Define a non-linear graph.

Answer: A non-linear graph is not a straight line. A non-linear graph is describable with the help of an equation, relating the 2 variables ‘x’ and ‘y’, which cannot be reorganized to: ‘y = mx + c’.

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