Standard #: MAFS.912.S-ID.3.7 (Archived Standard)

Students are asked to interpret the meaning of the slope of the graph of a linear model.

Students are asked to interpret the meaning of the slope of the graph of a linear model.

Students are asked to interpret the intercept of a linear model of life expectancy data.

Students are asked to interpret the meaning of the constant term in a linear model.

This is an introductory lesson designed to help students have a better understanding of the interpretation of the slope (rate of change) of a graph. 

This is an introductory lesson designed to help students have a better understanding of the interpretation of the slope (rate of change) of a graph. 

The changing climate is an important topic for both scientific analysis and worldly knowledge. This lesson uses data collected by the National Snow and Ice Data Center to create and use mathematical models as a predictive tool and do critical analysis of sea ice loss.

This is lesson 3 of 3 in the Slope Intercept unit. This lesson introduces similar triangles to explain why slope is the same between any two points on a non-vertical line. In this lesson students perform an activity to determine that slope is constant throughout a line and students will discover the slope for vertical and horizontal lines.

Students investigate the amount of space that could be saved by flattening cardboard boxes. The analysis includes linear graphs and regression analysis along with discussions of slope and a direct variation phenomenon.

Students create scatter plots, calculate a regression equation using technology, and interpret the slope and y-intercept of the equation in the context of the data. This review lesson relates graphical and algebraic representations of bivariate data.

This lesson allows the students to connect the science of cricket chirps to mathematics. In this lesson, students will collect real data using the CD "Myths and Science of Cricket Chirps" (or use supplied data), display the data in a graph, and then find and use the mathematical model that fits their data.

Who doesn't want to save money? In this lesson, students will learn how a better credit score will save them money. They will use a scatter plot to see the relationship between credit scores and car loan interest rates. They will determine a line of fit equation and interpret the slope and y-intercept to make conclusions about interest and credit scores.

This lesson provides the students with scatter plots, lines of best fit and the linear equations to practice interpreting the slope and y-intercept in the context of the problem.

This lab exploration provides students with an opportunity to examine the relationship between the amount a linear spring is stretched and the restoring force that acts to return the spring to its rest length. This concept is central to an understanding of elastic potential energy in mechanical systems and has implications in the study of a large array of mechanical and electromagnetic simple harmonic oscillators.

Students will enjoy this project lesson that allows them to choose and collect their own data. They will create a scatter plot and find the line of fit. Next they write interpretations of their slope and y-intercept. Their final challenge is to calculate residuals and conclude whether or not their data is consistent with their linear model.

Students create scatter plots, and lines of fit, and then calculate the correlation coefficient. Students analyze the results and make predictions. This lesson includes step-by-step directions for calculating the correlation coefficient using Excel, GeoGebra, and a TI-84 Plus graphing calculator. Students will make predictions for the number of views of a video for any given number of weeks on the charts.

Students will interpret the meaning of slope and y-intercept in a wide variety of examples of real-world situations modeled by linear functions.

This lesson uses real-world examples to practice interpreting the slope and y-intercept of a linear model in the context of data. Students will collect data, graph a scatter plot, and use spaghetti to identify a line of fit. A PowerPoint is included for guidance throughout the lesson and guided notes are also provided for students.

Students use real-world data to construct and interpret scatter plots using technology. Students will create a scatter plot with a line of fit and a function. They describe the relationship of bivariate data. They recognize and interpret the slope and y-intercept of the line of fit within the context of the data.

This lesson consists of using data to make scatter plots, identify the line of fit, write its equation, and then interpret the slope and the y-intercept in context. Students will also use the line of fit to make predictions.

This lesson will not only reinforce students understanding of slope and y-intercept, but will also ensure the students understand how it can be modeled in a real world situation. The focus of this lesson is to emphasize that slope is a rate of change and the y-intercept the value of y when x is zero. Students will be able to read a problem and create a linear equation based upon what they read. They will then make predictions based upon this information.

This lesson is on motion of objects. Students will learn what factors affect the speed of an object through experimentation with gumballs rolling down an incline. The students will collect data through experimenting, create graphs from the data, interpret the slope of the graphs and create equations of lines from data points and the graph. They will understand the relationship of speed and velocity and be able to relate the velocity formula to the slope intercept form of the equation of a line.

In this lesson, students will experimentally determine whether an acid/base neutralization reaction is endothermic or exothermic. They will also use their results to identify the limiting reactant at various times in the process and calculate the concentration of one of the reactants.

Students will sketch and interpret the line of fit and then describe the correlation of the data. Students will determine if there’s a correlation between foot size and height by collecting data.

Students will graph scatterplots and draw a line of fit. Next, students will write an equation for the line and use it to interpret the slope and y-intercept in context. Students will also use the graph and the equation to make predictions.

This is an introductory lesson designed to help students have a better understanding of the interpretation of the slope (rate of change) of a graph.

Students use data collection from their spaghetti bridge activity to write linear equations, graph the data, and interpret the data.

The lesson teaches students about an important characteristic of lines: their slope. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero, or undefined. Students get an explanation of when and how these different types of slopes occur. Finally, students learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another.

Prerequisite knowledge: Students must know how to graph points on the Cartesian plane. They must be familiar with the x- and y-axis on the plane in both the positive and negative directions.

Students will be comparing hybrid-electric vehicles (HEV) versus gasoline-powered vehicles. They will research the benefits of owning a HEV while also analyzing the cost effectiveness.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Students will construct a scatter plot from given data. They will identify the correlation, sketch an approximate line of fit, and determine an equation for the line of fit. They will explain the meaning of the slope and y-intercept in the context of the data and use the line of fit to interpolate and extrapolate values.

Learn what slope is in mathematics and how to calculate it on a graph and with the slope formula in this interactive tutorial.

In this video, Eugene Domack explains how past Antarctic ice sheet movement rates allow us to understand sea level changes. Video funded by NSF grant #: OCE-1502753.

Download the CPALMS Perspectives video student note taking guide.

Shark researcher, Chip Cotton, discusses the use of regression lines, slope, and determining the strength of the models he uses in his research.

Download the CPALMS Perspectives video student note taking guide.

The purpose of this task is to assess ability to interpret the slope and intercept of the line of fit in context.

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.

Linear equations can be used to solve many types of real-word problems. In this episode, the water depth of a pool is shown to be a linear function of time and an equation is developed to model its behavior. Unfortunately, ace Algebra student A. V. Geekman ends up in hot water anyway.

Learn what slope is in mathematics and how to calculate it on a graph and with the slope formula in this interactive tutorial.

The purpose of this task is to assess ability to interpret the slope and intercept of the line of fit in context.

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.

Linear equations can be used to solve many types of real-word problems. In this episode, the water depth of a pool is shown to be a linear function of time and an equation is developed to model its behavior. Unfortunately, ace Algebra student A. V. Geekman ends up in hot water anyway.

The purpose of this task is to assess ability to interpret the slope and intercept of the line of fit in context.

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.