1. Identify the graph that represents a direct variation.

2. Select the graph that represents a linear relationship that isn’t proportional.

3. Which graph represents the equation $ y=-2? $

4. Identify the correct graph for this equation: $ y=x-2 $

Types of Graphs - Math Steps, Examples & Questions

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Types of graphs

Here you will learn about types of graphs, including points on the coordinate plane, linear graphs, plotting linear equations, and interpreting linear graphs.

Students first learn about graphs in the early grades when gathering and plotting data on line graphs and circle graphs with their work in measurement and data.

In the 6th grade, students begin to work with the coordinate plane in order to graph ordered pairs with their work in expressions and equations.

Every week, we teach lessons on different types of graphs to students in schools and districts across the US as part of our online one-on-one math tutoring programs. On this page we’ve broken down everything we’ve learnt about teaching this topic effectively.

What are types of graphs?

Types of graphs are visual representations of mathematical relationships. Types of graphs can include points, straight lines, curves, polygons, and circles, depending on the type of graph that is needed.

Graphing is a major component to the understanding of mathematics because it provides a visual representation of a mathematical relationship. Let’s look at different types of charts and graphs.

Name of graph	Sample of graph
Pie graph: ● Also known as a circle graph or pie chart ● A graphical representation or visual representation of data that is displayed in a circle. ● The data is typically in percent form.
Pictograph: ● Also known as pictogram ● Displays data in the form of pictures or symbols. ● The pictures or symbols represent the frequency of the data.
Bar Graph: ● Also known as bar chart or column chart ● Displays data points and frequency distributions. ● A stacked bar chart takes the set of data and divides it into different categories.
Line Graph: ● Also known as a line chart or line plot ● Displays continues data over a period of time ● Shows how the data increases and decreases.
Box and whisker plot: ● Also known as a box plot ● Represents numerical data on a number line. ● Displays median, interquartile range, minimum value and maximum value and any outliers.
Coordinate plane: ● Used to represent ordered pairs in the form of $katex is not defined$ ● Has horizontal axis called the $katex is not defined$ -axis and a vertical axis called the $katex is not defined$ -axis. ● Used to plot algebraic equations such as linear equations, quadratic equations, exponential equations, polynomial equations, etc…
Scatter plot: ● Also known as a scatter graph ● Displays data in the form of ordered pairs on the coordinate plane.
Venn diagram: ● Shows the relationship between data sets.

[FREE] Types Of Graphs Worksheet (Grade 6 to High School)

Check your grade 6 to high school students’ understanding of recognizing and plotting types of graphs. 15 questions with answers to easily identify learning gaps!

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[FREE] Types Of Graphs Worksheet (Grade 6 to High School)

Check your grade 6 to high school students’ understanding of recognizing and plotting types of graphs. 15 questions with answers to easily identify learning gaps!

DOWNLOAD FREE

Coordinate plane and plotting points

Let’s focus on the coordinate plane and how it is used.


$katex is not defined$ axis and $katex is not defined$ axis: The $katex is not defined$ axis and $katex is not defined$ axis are straight lines that make up the coordinate plane, where each point on the plane can be represented as a coordinate of the form $katex is not defined$ ● The $katex is not defined$ -axis is a horizontal line (left to right). ● The $katex is not defined$ -axis is a vertical line (up and down). ● The $katex is not defined$ -axis and $katex is not defined$ -axis intersect at the origin (0,0).

$katex is not defined$ axis and $katex is not defined$ axis:

The $katex is not defined$ axis and $katex is not defined$ axis are straight lines that make up the coordinate plane, where
each point on the plane can be represented as a coordinate of the form $katex is not defined$
● The $katex is not defined$ -axis is a horizontal line (left to right).
● The $katex is not defined$ -axis is a vertical line (up and down).
● The $katex is not defined$ -axis and $katex is not defined$ -axis intersect at the origin (0,0).


The $katex is not defined$ axis and $katex is not defined$ axis divides the plane into $katex is not defined$ parts, or $katex is not defined$ quadrants.	Points on the coordinate plane are made up of an $katex is not defined$ -coordinate and a $katex is not defined$ -coordinate and is written as $katex is not defined$ Plotting the point $katex is not defined$ on the coordinate plane

Each quadrant has unique characteristics.

Quadrant I	Quadrant II	Quadrant III	Quadrant IV
$katex is not defined$ $katex is not defined$ positive $katex is not defined$ positive	$katex is not defined$ $katex is not defined$ negative $katex is not defined$ positive	$katex is not defined$ $katex is not defined$ negative $katex is not defined$ negative	$katex is not defined$ $katex is not defined$ positive $katex is not defined$ negative

Step by step guide: Coordinate plane

The coordinate plane can be used to find the distance between points.

For example, plot the coordinates $katex is not defined$ and $katex is not defined$ on the coordinate plane and then find the distance between the points.

Plot the points and then count the units between the points.

Count the number of units from point $katex is not defined$ to point $katex is not defined$ It is $katex is not defined$ units. You can also find the absolute value of the difference to find the distance.

$katex is not defined$

Step by step guide: Plot points on a graph.

Linear graphs

Linear graphs are graphs that form straight lines on a coordinate plane.

For example, the graphs below show linear graphs because they are straight lines.

Linear graphs can represent proportional relationships if they contain the point $katex is not defined$

If a linear graph is proportional, the points have a common ratio in the form of $katex is not defined$

Graph $katex is not defined$ is a proportional relationship because the line passes through the origin, $katex is not defined$ and the points have a common ratio of $katex is not defined$

Graph $katex is not defined$ is not a proportional relationship because the line does not pass through the origin and the points do not have a common ratio.

Step-by-step guide: Linear graphs

Equations can represent linear relationships and be graphed on the coordinate plane.

For example, graph the equation $katex is not defined$ on the coordinate graph by making a table of values.

The $katex is not defined$ -coordinate is the independent variable, so you can choose any value you want for $katex is not defined$ Substitute the values of $katex is not defined$ into the equation to find the $katex is not defined$ -coordinates.

The $katex is not defined$ -coordinate is the dependent variable because it’s value depends on the $katex is not defined$ value.

$katex is not defined$	$katex is not defined$	$katex is not defined$	$katex is not defined$
$katex is not defined$	$katex is not defined$	$katex is not defined$	$katex is not defined$
$katex is not defined$	$katex is not defined$	$katex is not defined$	$katex is not defined$
$katex is not defined$	$katex is not defined$	$katex is not defined$	$katex is not defined$

The equation $katex is not defined$ is a linear graph, and it passes through the origin.

Also, the ratio of the points in the form of $katex is not defined$ is $katex is not defined$

$katex is not defined$

Direct variation

Linear equations in the form of $katex is not defined$ represent proportional relationships where $katex is not defined$ is the common ratio, which also represents the constant of proportionality.

The equation $katex is not defined$ can be called direct variation.

Direct variation is when $katex is not defined$ the independent variable, varies directly with $katex is not defined$ the dependent variable. This means that the ratio between the $katex is not defined$ -coordinate and the $katex is not defined$ -coordinate is constant.

For example, if $katex is not defined$ and $katex is not defined$ vary directly, find the equation of direct variation when $katex is not defined$ and $katex is not defined$

The $katex is not defined$ -coordinate and $katex is not defined$ -coordinate vary directly, which means the ratio of the $katex is not defined$ and $katex is not defined$ coordinates is the same or constant.

$katex is not defined$

Since $katex is not defined$ , the equation of direct variation is $katex is not defined$ .

Step by step guide: Direct Variation

Graphs can be used to represent real world situations where you may be asked to interpret the graph.

Make sure to look at the key information on the graph. You may be asked to read a value from the graph, interpret a point on the graph, or find a constant of variation (proportionality) from the graph.

For example, the graph represents a proportional, linear relationship where the distance you are from lightning varies directly with the time it takes for you to hear the thunder. Interpret the point $katex is not defined$ from the graph.

Step-by-step guide: Interpreting graphs

What are types of graphs?

Common Core State Standards

How does this relate to 6th grade math, 7th grade math, and 8th grade math?

Grade 6 – Number System (6.NS.C.6.b)
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

Grade 6 – The Number System (6.NS.C.8)
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Grade 6 – Geometry (6.G.A.3)
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Grade 6 – Expressions and Equations (6.EE.C.9)
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

Grade 7 – Ratios and Proportional Relationships (7.RP.A.2.b)
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Grade 7 – Ratios and Proportional Relationships (7.RP.A.2.d)
Explain what a point $katex is not defined$ on the graph of a proportional relationship means in terms of the situation, with special attention to the points $katex is not defined$ and $katex is not defined$ where $katex is not defined$ is the unit rate.

Grade 8 – Expressions and Equations (8.EE.B.5)
Graph proportional relationships, interpreting the unit rate as the slope of the graph.

How to recognize types of graphs

In order to recognize types of graphs:

Identify the graph as a linear relationship or a non-linear relationship.
Identify if the linear relationship represents direct variation.

Recognize types of graphs examples

Example 1: recognize the types of graphs

Does the graph represent a linear relationship?

Identify the graph as a linear relationship or a non-linear relationship.

The graph is a non-linear relationship because it does not form a straight line.

2Identify if the linear relationship represents direct variation.

The graph is not linear.

Example 2: recognize the types of graphs

Does the graph represent a linear relationship?

Identify the graph as a linear relationship or a non-linear relationship.

Show step

The graph is a linear relationship because it forms a straight line.

Identify if the linear relationship represents direct variation.

Show step

The graph is a linear relationship but it does not represent direct variation because the line does not pass through the origin, $katex is not defined$

Example 3: recognize the types of graphs

Classify each of the graphs as linear or non-linear.

Identify the graph as a linear relationship or a non-linear relationship.

Show step

Graph A is a non-linear relationship because it is not a straight line.

Graph B is a linear relationship because it forms a straight line.

Graph C is a linear relationship because it forms a straight line.

Graph D is a non-linear relationship because it does not form a straight line.

Identify if the linear relationship represents direct variation.

Show step

Graph C is a linear graph that represents a direct variation because the line passes through the origin.

How to plot types of graphs

In order to plot different types of graphs

Complete the table of values.
Plot the coordinates.
Draw a straight line through the points.

Example 4: plot types of graphs

Plot the graph represented by the equation $katex is not defined$

Complete the table of values.

Show step

Substitute the values of $katex is not defined$ into the equation, $katex is not defined$ Write the values of $katex is not defined$ in the table.

Plot the coordinates.

Show step

Draw a straight line through the points.

Show step

Example 5: plot types of graphs

Plot the graph represented by the equation $katex is not defined$

Complete the table of values.

Show step

In this case the the $katex is not defined$ value will be $katex is not defined$ for each $katex is not defined$ value.

Plot the coordinates.

Show step

Draw a straight line through the points.

Show step

Example 6: plot types of graphs

Plot the graph represented by the equation $katex is not defined$

Complete the table of values.

Show step

Substitute the values of $katex is not defined$ into the equation, $katex is not defined$ Write the values of $katex is not defined$ in the table.

Plot the coordinates.

Show step

Draw a straight line through the points.

Show step

Teaching tips for types of graphs

Creating and interpreting graphs is an essential skill in mathematics. Graphs help to organize mathematical information while also providing a visual model. Be sure to emphasize these skills in the classroom as they lead to data literacy.

Using discovery-based activities which provide students with the opportunity to compare and contrast graphs and connect linear equations to the graphs they represent helps students formulate their own understanding.

Infuse graphs that represent real world situations so that students can connect the math concepts to the world around them.

Easy mistakes to make

Making arithmetic errors when substituting $katex is not defined$ values into the equation which produces incorrect $katex is not defined$ -values

Plotting a point incorrectly
If there is a point that does not join up with the other points when you draw a smooth line, go back and check the coordinate. In the example below, there is a point that does not lie on the line so needs checking.

Practice types of graphs questions

Types of Graphs practice question 1 image 1

Types of Graphs practice question 1 image 2

Types of Graphs practice question 1 image 3

Types of Graphs practice question 1 image 4

The linear graph that passes through the origin represents direct variation.

Types of Graphs practice question 2 image 1

Types of Graphs practice question 2 image 2

Types of Graphs practice question 2 image 3

Types of Graphs practice question 2 image 4

The graph shows a linear relationship that does not pass through the origin which means that it is a linear relationship that is not proportional.

Types of Graphs practice question 3 image 1

Types of Graphs practice question 3 image 2

Types of Graphs practice question 3 image 3

Types of Graphs practice question 3 image 4

Make a table of values for the equation $katex is not defined$

The $katex is not defined$ -value is $katex is not defined$ for each of the different $katex is not defined$ -values.

Types of Graphs practice question 3 image 5

Plot the points.

Types of Graphs practice question 3 image 6

Then connect the point with a smooth line.

Types of Graphs practice question 3 image 7

Types of Graphs practice question 4 image 1

Types of Graphs practice question 4 image 2

Types of Graphs practice question 4 image 3

Types of Graphs practice question 4 image 4

Make a table of values for the equation $katex is not defined$

Substitute the $katex is not defined$ values into the equation to find the $katex is not defined$ values.

Types of Graphs practice question 4 image 5

Plot the points.

Types of Graphs practice question 4 image 6

Connect the points.

Types of Graphs practice question 4 image 7

katex is not defined

katex is not defined

katex is not defined

katex is not defined

The linear equation $katex is not defined$ represents a proportional relationship or direct variation because it is in the form of $katex is not defined$ where $katex is not defined$

Also, it’s the only equation that has the point $katex is not defined$

katex is not defined

katex is not defined

katex is not defined

katex is not defined

Looking at the graph you can see that it does not pass through the origin so it will not be a proportional relationship.

Therefore, the equation will not be in the form of $katex is not defined$

When you substitute values for $katex is not defined$ into the equation, $katex is not defined$ the point $katex is not defined$ exists on the line which matches the graph.

Types of graphs FAQs

Are all graphs straight lines?

No, as you move through high school you will graph curves such as quadratic functions, exponential functions, and other polynomial functions.

Is there a special equation for linear graphs that do not represent direct variation?

Yes, when you learn algebra you will learn about linear equations in slope-intercept form, point-slope form, and standard form.

Are there other ways to graph a linear equation other than making a table of values?

Making a table of values is a method that will always work when plotting a linear equation. However, in algebra you will learn other methods that require less arithmetic such as using slope, $katex is not defined$ -intercept, and $katex is not defined$ -intercept.

What are the most common types of graphs?

There are many different kinds of graph types. In algebra, you will use the coordinate plane and analyze scatter plots. In a statistics class, you will use statistical graphs and charts depending on the different data collected.

What is a histogram?

A histogram is used to graph frequency distributions and is quite similar to a bar graph.

Do all graphs and charts have to be done by hand?

No, there are many digital tools you can use to graph data sets such as excel, Google sheets, Desmos, etc.

Do you learn about all the different types of graphs and charts in algebra?

No, in high school you will be exposed to statistics where you learn in depth about the various ways to display and analyze data. Other charts and graphs you will learn about are waterfall charts in excel, area graphs, bubble graphs, to name a few.

The next lessons are

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