Use the following Media4Math resources with this Illustrative Math lesson.
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Definition--Direct Variation | Direct Variation
TopicLinear Functions DefinitionDirect variation describes a linear relationship between two variables where one variable is a constant multiple of the other, expressed as y = kx, where k is the constant of variation. DescriptionDirect variation is a fundamental concept in linear functions, illustrating how one variable changes proportionally with another. The constant of variation, 𝑘 k, represents the rate of change. In real-world scenarios, direct variation can model relationships such as speed and distance, where distance traveled varies directly with time at a constant speed. Understanding this concept is crucial in fields like physics and engineering. |
Applications of Linear Functions | |
Definition--Linear Function Concepts--Linear Function Tables | Linear Function Tables
TopicLinear Functions DefinitionLinear function tables display the input-output pairs of a linear function, showing how the dependent variable changes with the independent variable. DescriptionLinear function tables are useful tools for understanding and analyzing linear relationships. They provide a clear way to see how changes in the input (independent variable) affect the output (dependent variable). |
Applications of Linear Functions and Graphs of Linear Functions | |
Definition--Ratios, Proportions, and Percents Concepts--The Constant of Proportionality | The Constant of ProportionalityTopicRatios, Proportions, and Percents DefinitionThe constant of proportionality is the constant value that relates two proportional quantities. DescriptionThe constant of proportionality is a fundamental concept in mathematics, particularly in linear relationships and direct variation. For example, in the equation y = kx, k is the constant of proportionality that relates y and x. This concept is crucial in fields like physics, where it is used to describe relationships such as speed (distance/time). |
Proportions | |
Definition--Variables, Unknowns, and Constants--Constant of Proportionality | Definition--Variables, Unknowns, and Constants--Constant of Proportionality
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns | |
Desmos Activity: Exploring Hooke's Law | Explore Hooke's Law using this Desmos graphing calculator activity. In this activity explore linear functions of the form y = mx. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file. Related Resources To see additional resources on this topic click on the Related Resources tab above. Desmos Collection To see the complete collection of Desmos Resources click on this link. |
Graphs of Linear Functions and Proportions | |
INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter | INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter
In this Algebra Application, students study the direction between diameter and circumference of a circle. Through measurement and data gathering students analyze the line of best fit and explore ways of calculating pi. The math topics covered include: Mathematical modeling, Linear functions, Data gathering and analysis, Ratios, Direct variation. This is a great back-to-school activity for middle school or high school students. This is also a great crossover activity that ties algebra and geometry. |
Applications of Linear Functions, Applications of Ratios, Proportions, and Percents and Applications of Circles | |
Instructional Resource: Applications of Linear Functions: Circumference vs. Diameter | In this Slide Show, apply concepts of linear functions to the context of circumference vs. diameter. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions | |
Instructional Resource: Applications of Linear Functions: Cost vs. Time | In this Slide Show, apply concepts of linear functions to the context of cost vs. time data and graphs. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions | |
Instructional Resource: Applications of Linear Functions: Hooke's Law | In this Slide Show, apply concepts of linear functions to the context of Hooke's law. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions and Proportions | |
Instructional Resource: Applications of Linear Functions: Hooke's Law | In this Slide Show, apply concepts of linear functions to the context of Hooke's law. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions and Proportions | |
Math Clip Art--Applications of Linear Functions: Hooke's Law 01 | Math Clip Art--Applications of Linear Functions: Hooke's Law 01TopicLinear Functions DescriptionThis image serves as the title card for a series of illustrations demonstrating applications of linear functions, specifically focusing on Hooke's Law. The series, comprising eight images, explores the relationship between force and displacement in springs, showcasing how linear models can represent real-world phenomena. |
Graphs of Linear Functions, Slope-Intercept Form and Proportions | |
Math Clip Art--Applications of Linear Functions: Hooke's Law 02 | Math Clip Art--Applications of Linear Functions: Hooke's Law 02TopicLinear Functions DescriptionThis image is part of a series illustrating applications of linear functions, focusing on Hooke's Law. It depicts a spring before and after being stretched by a weight, visually representing the fundamental concept of Hooke's Law. The illustration shows a spring in its original state and then stretched by an object of mass m, extending by a length x. This visual representation helps students understand the relationship between the applied force (weight) and the resulting displacement of the spring, which forms the basis of the linear function in Hooke's Law. |
Graphs of Linear Functions, Slope-Intercept Form and Proportions | |
Math Clip Art--Applications of Linear Functions: Hooke's Law 03 | Math Clip Art--Applications of Linear Functions: Hooke's Law 03TopicLinear Functions DescriptionThis image is a continuation of the series on applications of linear functions, specifically illustrating Hooke's Law. It builds upon the previous image by introducing the mathematical equation F(x) = kx, which is the core of Hooke's Law. The illustration shows that when a spring is stretched a distance x, a force F(x) is generated that is proportional to x. This visual representation, combined with the equation, helps students understand the linear relationship between force and displacement in springs. |
Graphs of Linear Functions, Slope-Intercept Form and Proportions | |
Math Clip Art--Applications of Linear Functions: Hooke's Law 04 | Math Clip Art--Applications of Linear Functions: Hooke's Law 04TopicLinear Functions DescriptionThis image is part of a series demonstrating applications of linear functions, focusing on Hooke's Law. It presents a practical application of the law by showing a data table alongside a weight scale, illustrating how Hooke's Law applies to everyday objects. |
Graphs of Linear Functions, Slope-Intercept Form and Proportions | |
Math Clip Art--Applications of Linear Functions: Hooke's Law 06 | Math Clip Art--Applications of Linear Functions: Hooke's Law 06TopicLinear Functions DescriptionThis image is part of a series demonstrating applications of linear functions, specifically focusing on Hooke's Law. It builds upon the previous images by introducing the general form of the linear function equation that describes the relationship observed in the weight scale experiment. |
Graphs of Linear Functions, Slope-Intercept Form and Proportions | |
Math Clip Art--Applications of Linear Functions: Hooke's Law 07 | Math Clip Art--Applications of Linear Functions: Hooke's Law 07TopicLinear Functions DescriptionThis image is part of a series illustrating applications of linear functions, focusing on Hooke's Law. It builds upon previous images by demonstrating how to calculate the spring constant 'k' using the data collected from the weight scale experiment. Note: Here is the link to the video referenced: https://www.media4math.com/library/42143/asset-preview |
Graphs of Linear Functions, Slope-Intercept Form and Proportions | |
Math Clip Art--Applications of Linear Functions: Hooke's Law 08 | Math Clip Art--Applications of Linear Functions: Hooke's Law 08TopicLinear Functions DescriptionThis image represents the culmination of our exploration into applications of linear functions, specifically focusing on Hooke's Law. It serves as the final piece in a series of eight images, tying together all the concepts we've examined throughout this study of spring behavior and weight measurement. |
Graphs of Linear Functions, Slope-Intercept Form and Proportions | |
Math Clip Art--Linear Function Tables 01 | Math Clip Art--Linear Function Concepts--Linear Function Tables 01TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, specifically focusing on linear function tables. It serves as a title card for a set of 10 clip art images that explore linear functions in tabular and graph form. This visual introduction sets the stage for understanding how linear functions can be represented and analyzed using tables. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Function Tables 02 | Math Clip Art--Linear Function Concepts--Linear Function Tables 02TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, focusing on linear function tables. It presents a data table demonstrating that a linear function table shows a common difference for values of f(x). This visual representation helps students understand the fundamental characteristic of linear functions - the constant rate of change. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Function Tables 03 | Math Clip Art--Linear Function Concepts--Linear Function Tables 03TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, specifically linear function tables. It builds on the previous image by showing that the common difference in a linear function can also be negative. This concept is crucial for understanding decreasing linear functions and their representation in tabular form. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Function Tables 04 | Math Clip Art--Linear Function Concepts--Linear Function Tables 04TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, focusing on linear function tables. It presents a new version of the previous table, this time demonstrating that the common difference can also be zero. This concept introduces students to constant functions, a special case of linear functions where the output remains the same regardless of the input. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Function Tables 05 | Math Clip Art--Linear Function Concepts--Linear Function Tables 05TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, focusing on the relationship between linear function tables and graphs. It shows both a data table and a linear graph of data points, demonstrating that the graph of a Linear Function Table is a series of collinear points. This visual representation helps students connect tabular and graphical representations of linear functions. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Function Tables 06 | Math Clip Art--Linear Function Concepts--Linear Function Tables 06TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, focusing on linear function tables and their corresponding graphs. It presents a variation of the previous image with a new set of data, demonstrating that when the common difference is positive, the orientation of the graph is upward from left to right. This helps students understand the concept of positive slope in linear functions. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Function Tables 07 | Math Clip Art--Linear Function Concepts--Linear Function Tables 07TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, focusing on linear function tables and their corresponding graphs. It shows a variation of the previous image with a new set of data, demonstrating that when the common difference is negative, the orientation of the graph is downward from left to right. This helps students understand the concept of negative slope in linear functions. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Function Tables 08 | Math Clip Art--Linear Function Concepts--Linear Function Tables 08TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, focusing on linear function tables and their corresponding graphs. It presents a variation of the previous image with a new set of data, showing that when the common difference is zero, the orientation of the graph is horizontal. This helps students understand the concept of zero slope in linear functions, also known as constant functions. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Function Tables 09 | Math Clip Art--Linear Function Concepts--Linear Function Tables 09TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, focusing on linear function tables. It shows a variation of the previous image with a new set of data, demonstrating that data gathered in a table can show a linear pattern. This concept helps students understand how to identify linear relationships from tabular data. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Function Tables 10 | Math Clip Art--Linear Function Concepts--Linear Function Tables 10TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, focusing on linear function tables and equations. It continues from the previous image, now including the equation f(x) = 0.5x - 3. This demonstrates that when a data set shows a linear pattern, it can be modeled by a linear function equation. This concept helps students understand the connection between tabular data and algebraic representations of linear functions. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 1 | Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 1TopicLinear Functions DescriptionThis image serves as a title card for a series of 10 clip art images that explore graphs of linear functions. It sets the stage for understanding how linear functions can be represented and analyzed graphically, introducing students to the visual aspect of these mathematical concepts. Using visual aids like this title card can help engage students and prepare them for the upcoming content. It provides a clear introduction to the topic and helps organize the learning material in a visually appealing way. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 10 | Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 10TopicLinear Functions DescriptionThis image is the final in a series illustrating key concepts in linear functions, focusing on the special case of vertical lines. It presents a variation of the previous image, now including a vertical line in the graph to demonstrate an important exception in linear functions. The image highlights that vertical lines are the only orientation not allowed in standard linear functions. This concept is crucial for students to understand the limitations of the slope-intercept form and to recognize when they need to use alternative representations. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 2 | Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 2TopicLinear Functions DescriptionThis image presents a data table alongside a linear graph with the slope and y-intercept labeled. It demonstrates the connection between tabular data and graphical representation of linear functions, helping students understand how numerical values translate into visual patterns. By incorporating this visual aid, teachers can enhance students' comprehension of the relationship between data points and their graphical representation. This image serves as a bridge between algebraic and geometric interpretations of linear functions. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 3 | Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 3TopicLinear Functions DescriptionThis image displays the general form of the slope-intercept equation (y = mx + b) with definitions of m and b. It provides a crucial link between the algebraic representation of linear functions and their graphical interpretation, helping students understand how each component of the equation affects the graph. Using this visual aid can significantly enhance students' understanding of the slope-intercept form and its relationship to linear graphs. It serves as a reference point for discussing how changes in m and b impact the line's appearance on a coordinate plane. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 4 | Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 4TopicLinear Functions DescriptionThis image continues from the previous one, now with labeled slope and y-intercept. It provides a visual breakdown of the general equation for a linear function, helping students understand this fundamental concept in a step-by-step manner. By using this visual aid, teachers can guide students through the process of understanding the slope-intercept form, reinforcing the connection between the algebraic definition and its graphical representation. This image is particularly useful for students who benefit from seeing mathematical concepts broken down into clear, visual steps. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 5 | Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 5TopicLinear Functions DescriptionThis image continues from the previous one, showing the slope calculation ratio. It demonstrates the importance of expressing slope as a ratio, which can help students more easily interpret and compare different linear functions. Incorporating this visual aid into lessons can help reinforce the concept of slope simplification and its importance in analyzing linear functions. It provides a clear example of how mathematical operations can be applied to make expressions more manageable and meaningful. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 6 | Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 6TopicLinear Functions DescriptionThis image presents a variation of the previous image with the y-intercept highlighted. It emphasizes the significance of the y-intercept in linear functions, helping students understand its role in determining where the line crosses the y-axis. By using this visual aid, teachers can draw attention to the y-intercept and its importance in interpreting linear functions. This image can help students connect the 'b' value in the slope-intercept form to its graphical representation, enhancing their understanding of how equations relate to graphs. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 7 | Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 7TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, focusing on the domain of linear functions. It continues from the previous images in the series, now highlighting the concept of domain in linear functions. The image presents a continuation of the previous graph with the domain identified. This visual representation helps students understand that the domain of a linear function extends infinitely in both directions on the x-axis. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 8 | Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 8TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, focusing on the range of linear functions. It presents a variation of the previous image, now highlighting the concept of range in linear functions. The image shows a variation of the previous graph with a label for the range. This visual aid helps students understand that the range of a linear function, like its domain, extends infinitely in both directions, but on the y-axis. |
Graphs of Linear Functions and Slope-Intercept Form | |
Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 9 | Math Clip Art--Linear Functions Concepts--Graphs of Linear Functions 9TopicLinear Functions DescriptionThis image is part of a series illustrating key concepts in linear functions, focusing on the various orientations of linear functions. It shows the slope-intercept equation alongside several linear graphs, emphasizing the infinite possibilities for linear function orientations. The image demonstrates that linear functions can have an infinite number of orientations, extending infinitely in all directions. This concept helps students understand the versatility and wide-ranging applications of linear functions in modeling real-world relationships. |
Graphs of Linear Functions and Slope-Intercept Form | |
Video Tutorial: Direct Variation | Video Tutorial: Direct Variation
Learn the basics of direct variations. Graphical and algebraic representations of direct variations are shown, as well as examples of such functions. |
Slope-Intercept Form | |
Video Tutorial: Hooke's Law | Video Tutorial: Hooke's Law
This YouTube video describes Hooke's Law, which is an application of linear functions of the form y = kx. |
Slope-Intercept Form and Proportions | |
Worksheet: Linear Function Tables, f(x) = ax, Set 1 | Worksheet: Linear Function Tables, f(x) = ax, Set 1
This is part of a collection of math worksheets on the topic of linear function tables. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Worksheet LibraryTo see the complete collection of Worksheets, click on this link. |
Applications of Linear Functions | |
Worksheet: Linear Function Tables, f(x) = ax, Set 10 | Worksheet: Linear Function Tables, f(x) = ax, Set 10
This is part of a collection of math worksheets on the topic of linear function tables. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Worksheet LibraryTo see the complete collection of Worksheets, click on this link. |
Applications of Linear Functions | |
Worksheet: Linear Function Tables, f(x) = ax, Set 11 | Worksheet: Linear Function Tables, f(x) = ax, Set 11
This is part of a collection of math worksheets on the topic of linear function tables. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Worksheet LibraryTo see the complete collection of Worksheets, click on this link. |
Applications of Linear Functions | |
Worksheet: Linear Function Tables, f(x) = ax, Set 12 | Worksheet: Linear Function Tables, f(x) = ax, Set 12
This is part of a collection of math worksheets on the topic of linear function tables. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Worksheet LibraryTo see the complete collection of Worksheets, click on this link. |
Applications of Linear Functions | |
Worksheet: Linear Function Tables, f(x) = ax, Set 13 | Worksheet: Linear Function Tables, f(x) = ax, Set 13
This is part of a collection of math worksheets on the topic of linear function tables. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Worksheet LibraryTo see the complete collection of Worksheets, click on this link. |
Applications of Linear Functions | |
Worksheet: Linear Function Tables, f(x) = ax, Set 14 | Worksheet: Linear Function Tables, f(x) = ax, Set 14
This is part of a collection of math worksheets on the topic of linear function tables. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Worksheet LibraryTo see the complete collection of Worksheets, click on this link. |
Applications of Linear Functions | |
Worksheet: Linear Function Tables, f(x) = ax, Set 15 | Worksheet: Linear Function Tables, f(x) = ax, Set 15
This is part of a collection of math worksheets on the topic of linear function tables. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Worksheet LibraryTo see the complete collection of Worksheets, click on this link. |
Applications of Linear Functions | |
Worksheet: Linear Function Tables, f(x) = ax, Set 16 | Worksheet: Linear Function Tables, f(x) = ax, Set 16
This is part of a collection of math worksheets on the topic of linear function tables. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Worksheet LibraryTo see the complete collection of Worksheets, click on this link. |
Applications of Linear Functions | |
Worksheet: Linear Function Tables, f(x) = ax, Set 17 | Worksheet: Linear Function Tables, f(x) = ax, Set 17
This is part of a collection of math worksheets on the topic of linear function tables. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Worksheet LibraryTo see the complete collection of Worksheets, click on this link. |
Applications of Linear Functions | |
Worksheet: Linear Function Tables, f(x) = ax, Set 18 | Worksheet: Linear Function Tables, f(x) = ax, Set 18
This is part of a collection of math worksheets on the topic of linear function tables. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Worksheet LibraryTo see the complete collection of Worksheets, click on this link. |
Applications of Linear Functions | |
Worksheet: Linear Function Tables, f(x) = ax, Set 19 | Worksheet: Linear Function Tables, f(x) = ax, Set 19
This is part of a collection of math worksheets on the topic of linear function tables. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Worksheet LibraryTo see the complete collection of Worksheets, click on this link. |
Applications of Linear Functions |