2.3.1 Finding Connections between Graphs and Equations

Algebra 12.3.1 Finding Connections between Graphs and Equations

Search for key terms or text.

Warm Up

Use the following information to answer questions 1 – 8. Here are graphs of two equations in a system.

Determine if each of these systems could be represented by the graphs. Be prepared to explain how you know.

${\begin{matrix} x + 2 y = 8 \\ x = - 5 \end{matrix}$

No.

How do you know?

Compare your answer:

Your answer may vary, but here is a sample. No, it cannot be represented by the graph. The graph for $x = - 5$ would be on the left side of the vertical axis, which is not what is shown.

${\begin{matrix} y = - 7 x + 13 \\ y = - 1 \end{matrix}$

No.

How do you know?

Compare your answer:

Your answer may vary, but here is a sample. No, it cannot be represented by the graph. The graph for $y = - 1$ would be a horizontal line, but no horizontal line is shown.

${\begin{matrix} 3 x = 8 \\ 3 x + y = 15 \end{matrix}$

Yes.

How do you know?

Compare your answer:

Your answer may vary, but here is a sample. Yes. $3 x = 8$ can be rearranged into $x = \frac{8}{3}$ . The graph for $x = \frac{8}{3}$ is a vertical line to the right of the vertical axis. $3 x + y = 15$ can be rewritten as $y = - 3 x + 15$ . Its graph has a negative slope and a positive $y$ -value for the vertical intercept.

${\begin{matrix} y = 2 x - 7 \\ 4 + y = 12 \end{matrix}$

No.

How do you know?

Compare your answer:

Your answer may vary, but here is a sample. No. The graph for $y = 2 x - 7$ would have a positive slope and a negative $y$ -value for the vertical intercept, neither of which matches the given graphs.

Previous Next

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

Use the information below to generate a citation. We recommend using a citation tool such as this one.
- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/2-3-1-finding-connections-between-graphs-and-equations

© 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.