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

3.1.4 Interpreting the Slope and Vertical Intercept of a Scatter Plot

Algebra 13.1.4 Interpreting the Slope and Vertical Intercept of a Scatter Plot

Search for key terms or text.

Activity

Here are several scatter plots.

Use scatter plot A to answer questions 1 - 2.

A scatter plot with a trend line that indicates a negative correlation. The x-axis represents age in years and extends from 0 to 24 with a scale of 2. The y-axis represents reaction time in milli-seconds and extends from 0 to 350 with a scale of 25.

Scatter plot A: y=9.25x+400y=9.25x+400

1.

Using the horizontal axis for xx and the vertical axis for yy, interpret the slope of the linear model in the situation shown.

2.

If the linear relationship continues to hold for the situation, interpret the yy-intercept of the linear model.

Use scatter plot B to answer questions 3 and 4.

Scatter plot B: y=0.44x+0.04y=0.44x+0.04

A scatter plot with a trend line that indicates a positive correlation. The x-axis represents number of bananas and extends from 0 to 7 with a scale of 1. The y-axis represents price in dollars and extends from 0 to 3.50 with a scale of 0.5.
3.

Using the horizontal axis for xx and the vertical axis for yy, interpret the slope of the linear model in the situation shown.

4.

If the linear relationship continues to hold for the situation, interpret the yy-intercept of the linear model.

Use scatter plot C to answer questions 5 - 6.

Scatter plot C: y=4x+87y=4x+87

A scatter plot with a trend line that indicates a positive correlation. The x-axis represents room size in square feet and extends from 0 to 500 with a scale of 50. The y-axis represents the cost to install flooring in dollars and extends from 0 to 2,200 with a scale of 100.
5.

Using the horizontal axis for xx and the vertical axis for yy, interpret the slope of the linear model in the situation shown.

6.

If the linear relationship continues to hold for the situation, interpret the yy-intercept of the linear model.

Use scatter plot D to answer questions 7 and 8.

Scatter plot D: y=2.4x+25.0y=2.4x+25.0

A scatter plot with a trend line that indicates a negative correlation. The x-axis represents the temperature in degrees Celsius and extends from 0 to 5.5 with a scale of 0.5. The y-axis represents the volume in cubic centimeters and extends from 0 to 24 with a scale of 2.
7.

Using the horizontal axis for xx and the vertical axis for yy, interpret the slope of the linear model in the situation shown.

8.

If the linear relationship continues to hold for the situation, interpret the yy-intercept of the linear model.

Are you ready for more?

Extending Your Thinking

Clare, Diego, and Elena collect data on the mass and fuel economy of cars at different dealerships.

Clare finds the line of best fit for data she collected for 12 used cars at a used car dealership. The line of best fit is y=91,000x+34.3y=91,000x+34.3 where xx is the car’s mass, in kilograms, and yy is the fuel economy, in miles per gallon.

Diego made a scatter plot for the data he collected for 10 new cars at a different dealership.

A scatter plot with a negative correlation. The x-axis represents mass measured in kilograms and extends from 1,200 to 2,400 with a scale of 200. The y-axis represents the fuel economy in miles per gallon and extends from 0 to 30 with a scale of 5.

Elena made a table for data she collected on 11 hybrid cars at another dealership.

mass (kilograms) fuel economy (miles per gallon)
1,100 38
1,200 39
1,250 35
1,300 36
1,400 31
1,600 27
1,650 28
1.

Interpret the slope and yy-intercept of Clare’s line of best fit in this situation.

2.

Diego looks at the data for new cars and used cars. He claims that the fuel economy of new cars decreases as the mass increases. He also claims that the fuel economy of used cars increases as the mass increases. Do you agree with Diego’s claims? Be prepared to show your reasoning.

3.

Elena looks at the data for hybrid cars and correctly claims that the fuel economy decreases as the mass increases. How could Elena compare the decrease in fuel economy as mass increases for hybrid cars to the decrease in fuel economy as mass increases for new cars? Be prepared to show your reasoning.

Self Check

The scatter plot below shows the results of a survey of eighth-grade students who were asked to report the number of hours per week they spend playing video games and the typical number of hours they sleep each night.



A SCATTER PLOT THAT SHOWS VIDEO GAME TIME IN HOURS PER WEEK ON THE X-AXIS AND SLEEP TIME IN HOURS PER NIGHT ON THE Y-AXIS. THE LINE DRAWN DECREASES FROM LEFT TO RIGHT.


Which of the following conclusions can you make looking at the data?

  1. There is not a trend between time spent on video games and sleep time.
  2. As video game time increases, sleep time decreases.
  3. As video game time decreases, sleep time decreases.
  4. As video game time increases, sleep time increases.

Additional Resources

Using Linear Models

The Monopoly board game is popular in many countries. The scatter plot below shows the distance from “Go” to a property (in number of spaces moving from “Go” in a clockwise direction) and the price of the properties on the Monopoly board. The equation of the line is P=8x+40P=8x+40, where PP represents the price (in Monopoly dollars) and xx represents the distance (in number of spaces).

A scatter plot that shows the "distance from go" in number of spaces on the x-axis and the price of a property in monopoly dollars on the y-axis. The line drawn increases from left to right.

The model shows that as the distance from “Go” increases, the price of the property increases.

The slope of the equation of the linear model is 8. This means that for every space from “Go,” the price of the property increases $8.

Notice this gives an estimate. The most expensive property is 39 spaces from “Go” and costs $400. The model would give the price to be y=8(39)+40y=8(39)+40 or $352.

The model gives a difference of $48 between the estimated price using the model and the actual price.

Try it

Try It: Using Linear Models

A scatter plot that shows the mean temperature, in degrees Fahrenheit, in July on the x-axis and the mean rainfall per year, in inches, on the y-axis. The line drawn increases from left to right. The x-axis representing the number of people extends from 65 to 80 with a scale of 0.5. The y-axis representing the noise level extends from 30 to 42 with a scale of 0.5.

Looking at the linear model above, what claim can be made?

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.