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Different Forms of Representation for a Relationship

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Lesson Focus

Different Forms of Representation for a Relationship


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You will explore various forms of representations for a relationship.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Create a table for a linear relationship.
  • Write the equation for a linear relationship.
  • Determine the appropriateness of using a table, graph, or equation to answer questions about a linear relationship.
  • Use information given in a table of a linear relationship to answer questions.
  • Use the equation of a linear relationship to answer questions.

Everything You'll Have Covered

Linear relationships can be identified by graphing values from a table.

Values that are presented in a table can be graphed to show the relationship between the values. For example, the table below represents the data in the following problem situation: A student is keeping a log of the amount of miles he runs every day. If he runs 5 miles per day, how many total miles will he have at the end of 4 days?

The top row represents the x values on the graph, and the bottom row represents the y values on the graph.

Notice that if you graph the x and y values you would get the following ordered pairs: day 1 (1, 5), day 2 (2, 10), day 3 (3, 15), and day 5 (4, 20).

Therefore, the relationship between the x-values and the y-values when graph form a straight line, thus a linear relationship.

Linear relationship is a relationship between two variables whose resulted graph on a coordinate plane is a straight line, meaning that there is a constant rate of change. In this example, the student runs 5 miles per day.

Writing the equation for a table of values.

Finding the pattern in the table is part of the equation. For example, if you can determine the pattern in the following table then you can use the pattern operation(s) to write the equation.

Notice that in the table above the relationship between the top and bottom column is described as multiplying by 5.

Therefore the equation would be y = 5x.

Writing an equation from a verbal statement.

Words like "per day" indicate a rate.

If a video store charges $2 per day, you can write the following equation (when d represents days): 2d.

If a competing video store has a $2 rental price plus $5 per day, you can write the equation 2 + 5d.

Representations of a linear relationship and their advantages.

There are different advantages of using the different representations of a relationship.

In relationships such as the ones used in the Activity Object where the prices of renting from two different stores are presented, the advantages are:


Using a table, it is easy to see the relation between the rental price and the number of days. Table also provides information in an organized manner but it is limited to only the values given. Therefore, it may not always be the best representation to use.


If you need information that is not provided in the table you can use the equation. Using an equation showing the relationship is more practical for calculating the price for any number of days.


Analyzing the graph helps us to see the general trends and make interpretation. The graph is useful because it allows you to see the relationship and determine when the cost is the same at both stores.

The following key vocabulary terms will be used throughout this Activity Object:

equation - a mathematical sentence that shows equality; includes an equal sign and usually includes variables

graph - a diagram or drawing that is used to display data

linear relationship - a relationship between two variables whose resulted graph on a coordinate plane is a straight line

relationship - an interaction between two sets of data that can be expressed in a graph, table or equation

table - information provided in an organized manner, but limited to only the values given

variable - a symbol or letter that stands for the value

Tutorial Details

Approximate Time 25 Minutes
Pre-requisite Concepts Students should be able to read tables, and write out and solve equations.
Course Algebra-1
Type of Tutorial Concept Development
Key Vocabulary equation, graph, relationship