Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Algebra 1

1.13.2 Creating Tables from Verbal Descriptions

Algebra 11.13.2 Creating Tables from Verbal Descriptions

Search for key terms or text.

Creating a Table of Values

For each situation in numbers 1 – 3, create a table of values with at least five columns to represent the situation.

1.

Julio works at a clothing store and makes $14 per hour.

2.

Jake had cavities at his last dentist visit. The dentist told him to brush his teeth for two minutes each time he brushes.

3.

For a fundraiser, Celia ran 5 miles on Monday (day 0) and then 3 miles every day after that.

Using a Table of Values to Write Equations

Table of values can be used to write equations. The tables from Creating a Table of Values all represent linear equations.

For 4 - 8, revisit the table from question 1 and write an equation to represent the table of values. Notice that columns for the x x and y y values are added.

x x 0 1 2 3 4 5
y y 0 14 28 42 56 70
4.

What is the starting value (when x = 0 x = 0 , what does y y equal)?

5.

How would you describe this value on the graph?

6.

What is the rate of change, or the change between the y y -values over the change between the x x -values?

7.

How would you describe this value on the graph?

8.

Using the information in questions 4 – 7, what would the equation be for the values represented by the table? Use slope-intercept form.

9.

Write an equation from the table of values created in question 2 of Creating a Table of Values.

Hint: (Work backward to find the value where x = 0 x = 0 using the pattern set in the table of values).

x x 0 1 2 3 4 5
y y ? 2 4 6 8 10
10.

Write an equation from the table of values created in question 3 of Creating a Table of Values

x x 0 1 2 3 4 5
y y ? 2 4 6 8 10

Video: Writing an Equation from a Table of Values

Watch the following video to learn more about writing equations from a table of values.

Create Your Own Situation

Think of your own situation that could be modeled by a linear equation. Create a table of values that represents that situation. Write your problem down then switch with a partner. Make a table of values for each other’s problems. Then, check your work together.

Next, plot the points of each table of values in a coordinate plane. Answer the questions after discussing with your partner:

1.

Describe the scenario created by your partner.

2.

Use Desmos to graph the table of values to represent your partner’s scenario.

Use the graphing tool or technology outside the course. Graph the equation that represents this scenario using the Desmos tool below.

3.

Does your partner’s data model a linear relationship or not? Describe how you determined your answer.

Are you ready for more?

Extending Your Thinking

1.

Kylie pays $20 to rent a scooter plus $0.40 per mile she drives the scooter. Create a table of values to represent Kylie’s situation starting with x = 0 x = 0 .

2.

Use the table to determine how much she has to pay after 5 miles.

Self Check

Which of the following equations could be represented by this table of values?

x 0 1 2 3
y 20 23 26 29
  1. y = 20 x + 3
  2. y = 20 x
  3. y = 1 3 x + 20
  4. y = 3 x + 20

Additional Resources

Writing Linear Equations from Tables

When writing linear equations from tables, it is important to identify the slope and the y y -intercepts from the table.

Example

Given the table, write an equation in slope-intercept form.

x x 0 1 2 3 4
y y 12 16 20 24 28

Step 1 - Identify the y y -intercept.

The y y -intercept is the starting value, when x = 0 x = 0 .

Looking at the table, when x = 0 x = 0 , the y y -value is 12, so this is the y y -intercept.

Step 2 - Identify the slope.

Slope is the change in y y over the change in x x .

The y y -values change by 4 each time. The x x -values change by 1 each time.

The slope is 4 1 4 1 or 4.

Step 3 - Write the equation in slope-intercept form.

Slope intercept form is y = m x + b y = m x + b , where m m is the slope and b b is the y y -intercept.

Substitute the values, y = 4 x + 12 y = 4 x + 12 .

Try it

Try It: Writing Linear Equations from Tables

Given the table, write an equation in slope-intercept form.

x x 0 1 2 3
y y 6 11 16 21
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.