Skip to ContentGo to accessibility page
OpenStax Logo
Algebra 1

3.1.3 Interpreting the Slope and Vertical Intercept of a Linear Model

Algebra 13.1.3 Interpreting the Slope and Vertical Intercept of a Linear Model

3.1.3 Interpreting the Slope and Vertical Intercept of a Linear Model

3.1.3 • Interpreting the Slope and Vertical Intercept of a Linear Model

Activity

The scatter plot shows the sale price of several food items, yy, and the cost of the ingredients used to produce those items, xx, as well as a line that models the data. The line is also represented by the equation y=3.48x+0.76y=3.48x+0.76.

1.

What is the predicted sale price of an item that has ingredients that cost $1.50? Be prepared to show your reasoning.

2.

What is the predicted ingredient cost of an item that has a sale price of $7? Be prepared to show your reasoning.

3.

What is the slope of the linear model?

4.

What does the slope value mean in this situation?

5.

What is the 𝑦-intercept of the linear model?

6.

What does the value of the yy-intercept mean in this situation?

7.

Does the value of the yy-intercept make sense in this situation?

Video: Using Linear Models

Watch the following video to learn more about how to use linear models.

Linear Models

Self Check

The scatter plot below shows the age (in years) and the price (in dollars) of used compact cars advertised in the local newspaper.


Nora drew a line to fit the data. What is the slope of her line, and what does it mean in the problem?

  1. − 1 1000 , for every year older the car is, it decreases 1 1000 of its value the year before.
  2. 1000 , for every year older the car is, its price increases 1000 dollars.
  3. 1000 , for every year older the car is, its price decreases 1000 dollars.
  4. − 1000 , for every year older the car is, its price decreases 1000 dollars.

Additional Resources

Interpreting a Linear Model

The scatter plot below shows the height and speed of some of the world’s fastest roller coasters. A line has been drawn to show a good fit for the data. 

The equation of the line drawn is S=0.11h+60S=0.11h+60.

What does this slope mean in the problem?

For every foot taller the roller coaster is, the speed increases 0.11 miles per hour.

Try it

Interpreting a Linear Model

Eight students were asked to estimate their score on a 10-point quiz. Their estimated and actual scores are given in the table below. Plot the points. Then sketch a line that fits the data.

Predicted Actual
6 6
7 7
7 8
8 8
7 9
9 10
10 10
10 9

Here are the points from the table plotted on a scatter plot, with the xx-axis being the predicted scores and the yy-axis being the actual scores.

1.

Tell what you would expect someone’s grade to actually be if they predicted their grade to be a 5 out of 10.

2.

What does the slope mean in this problem?

PreviousNext
Order a print copy
Citation/Attribution
Reuse and redistribution of this content in digital or print format:
  • 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 prior written permission.
  • This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License, which means that you can reuse and modify the material only for noncommercial purposes, must attribute OpenStax, and must distribute any derivative works under the same license.
  • Any commercial printing of this textbook, including using a local or custom printer, must be approved by OpenStax, and proper citation provided.
  • OpenStax-copyrighted images, activities, assessments, and similar components of this book are subject to the same licensing – CC-BY-NC-SA. They can be used for noncommercial purposes with attribution. Commercial use requires permission.
  • Permission requests: Anyone who intends to incorporate this content (including text, images, and other components) into large language models, use it in AI offerings, use it commercially (including in print), and/or has questions about another use case is welcome to complete our reuse request form.
Attribution information
  • If you are redistributing all or part of this book in a noncommercial 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 noncommercial digital format, then for every page that includes OpenStax content, you must license the derivative work under the same CC-BY-NC-SA license as the original, and 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

The information below includes the information needed to generate citations in most major styles (APA, MLA, etc.); you must reformat and organize the information as needed to fit the requirements of the style. Use the information below to generate a citation. We recommend using a citation tool such as this one.

© Apr 23, 2026 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, and Rice University name, and Rice University logo trademarks, or wordmarks are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.