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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 7 Unit 2

Introducing Proportional Relationships

Lesson 8: Comparing Relationships with Equations

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Math Video Definitions Collection: Linear Expressions, Functions, and Equations Math Video Definitions Collection: Linear Expressions, Functions, and Equations

Overview

This collection aggregates all the video definitions around the topic of Linear Expressions, Functions, and Equations terms and vocabulary. There are a total of 34 videos. This collection of resources is made up of downloadable MP4 files that you can easily incorporate into a presentation.

 

 

 

Slope-Intercept Form, Applications of Linear Functions, Graphs of Linear Functions, Point-Slope Form, Slope, Standard Form, Solving Systems of Equations, Proportions, Data Analysis, Variable Expressions, Functions and Their Inverses, Special Functions, Polynomial Expressions and Numerical Expressions
Algebra Applications Teacher's Guide: Linear Functions Algebra Applications Teacher's Guide: Linear Functions Algebra Applications Teacher's Guide: Linear Functions

This is the Teacher's Guide that accompanies Algebra Applications: Linear Functions.

This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Applications of Linear Functions
Algebra Nspirations Teacher's Guide: Linear Functions Algebra Nspirations Teacher's Guide: Linear Functions Algebra Nspirations Teacher's Guide: Linear Functions

This is the Teacher's Guide that accompanies Algebra Nspirations: Linear Functions.

This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Applications of Linear Functions
VIDEO: Algebra Nspirations: Functions and Relations VIDEO: Algebra Nspirations: Functions and Relations VIDEO: Algebra Nspirations: Functions and Relations

Functions are relationships between quantities that change. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video explores the definition of a function, its vocabulary and notations, and distinguishes the concept of function from a general relation. Multiple representations of functions are provided using the TI-Nspire, while dynamic visuals and scenarios put them into real-world contexts. Concepts explored: functions, relations, equations, quadratic functions, linear functions, multiple representations.

Applications of Functions and Relations, Quadratic Equations and Functions and Relations and Functions
VIDEO: Algebra Nspirations: Linear Functions VIDEO: Algebra Nspirations: Linear Functions VIDEO: Algebra Nspirations: Linear Functions

In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide real-world examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TI-Nspire. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slope-intercept form, point-slope form, solving linear equations.

Applications of Linear Functions
Closed Captioned Video:  Algebra Applications: Linear Functions, Segment 2: Cycling Closed Captioned Video: Algebra Applications: Linear Functions, Segment 2: Cycling Closed Captioned Video: Algebra Applications: Linear Functions, Segment 2: Cycling

Linear Expressions, Equations, and Functions

Linear Expressions
Special Functions and Applications of Linear Functions
Closed Captioned Video: Algebra Applications: Linear Functions Closed Captioned Video: Algebra Applications: Linear Functions Closed Captioned Video: Algebra Applications: Linear Functions

Linear Expressions, Equations, and Functions

Linear Expressions
Special Functions and Applications of Linear Functions
Closed Captioned Video: Algebra Applications: Linear Functions, Segment 1: Introduction Closed Captioned Video: Algebra Applications: Linear Functions, 1 Closed Captioned Video: Algebra Applications: Linear Functions, Segment 1: Introduction

Linear Expressions, Equations, and Functions

Linear Expres
Special Functions and Applications of Linear Functions
Closed Captioned Video: Algebra Applications: Linear Functions, Segment 3: Oil Exploration Closed Captioned Video: Algebra Applications: Linear Functions, 3 Closed Captioned Video: Algebra Applications: Linear Functions, Segment 3: Oil Exploration

Linear Expressions, Equations, and Functions

Linear Exp
Special Functions and Applications of Linear Functions
Closed Captioned Video: Algebra Applications: Linear Functions, Segment 4: Exercise Closed Captioned Video: Algebra Applications: Linear Functions, 4 Closed Captioned Video: Algebra Applications: Linear Functions, Segment 4: Exercise

Linear Expressions, Equations, and Functions

Linear Expression
Special Functions and Applications of Linear Functions
Closed Captioned Video: Algebra Nspirations: Functions and Relations Closed Captioned Video: Algebra Nspirations: Functions and Relations Closed Captioned Video: Algebra Nspirations: Functions and Relations

Functions are relationships between quantities that change. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video explores the definition of a function, its vocabulary and notations, and distinguishes the concept of function from a general relation. Multiple representations of functions are provided using the TI-Nspire, while dynamic visuals and scenarios put them into real-world contexts. Concepts explored: functions, relations, equations, quadratic functions, linear functions, multiple representations.

Applications of Functions and Relations, Conic Sections and Relations and Functions
Closed Captioned Video: Algebra Nspirations: Functions and Relations, Segment 1 Closed Captioned Video: Algebra Nspirations: Functions and Relations, 1 Closed Captioned Video: Algebra Nspirations: Functions and Relations, Segment 1

In this Investigation we explore the definition of a Relation. This video is Segment 1 of a 4 segment series related to Functions and Relations. Segments 1 and 2 are grouped together.

Applications of Functions and Relations, Conic Sections and Relations and Functions
Closed Captioned Video: Algebra Nspirations: Functions and Relations, Segment 3 Closed Captioned Video: Algebra Nspirations: Functions and Relations, 3 Closed Captioned Video: Algebra Nspirations: Functions and Relations, Segment 3

In this Investigation we look at functions. This video is Segment 3 of a 4 segment series related to Functions and Relations. Segments 3 and 4 are grouped together.

Applications of Functions and Relations, Conic Sections and Relations and Functions
Closed Captioned Video: Algebra Nspirations: Linear Functions Closed Captioned Video: Algebra Nspirations: Linear Functions Closed Captioned Video: Algebra Nspirations: Linear Functions

In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide real-world examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TI-Nspire. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slope-intercept form, point-slope form, solving linear equations.

Applications of Linear Functions
Closed Captioned Video: Algebra Nspirations: Linear Functions, Segment 1 Closed Captioned Video: Algebra Nspirations: Linear Functions, 1 Closed Captioned Video: Algebra Nspirations: Linear Functions, Segment 1

In this Investigation we look at linear models for objects moving at a constant speed. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 1 and 2 are grouped together.

Applications of Linear Functions
Closed Captioned Video: Algebra Nspirations: Linear Functions, Segment 3 Closed Captioned Video: Algebra Nspirations: Linear Functions, 3 Closed Captioned Video: Algebra Nspirations: Linear Functions, Segment 3

In this Investigation we look at a linear regression for carbon dioxide emission data. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 3 and 4 are grouped together.

Applications of Linear Functions
Closed Captioned Video: Linear Functions: Negative Slope, Negative y-Intercept Closed Captioned Video: Linear Functions: Negative Slope, Negative y-Intercept Closed Captioned Video: Linear Functions: Negative Slope, Negative y-Intercept

Video Tutorial: Linear Functions: Negative Slope, Negative y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a negative y-intercept.

Graphs of Linear Functions
Closed Captioned Video: Linear Functions: Negative Slope, Positive y-Intercept Closed Captioned Video: Linear Functions: Negative Slope, Positive y-Intercept Closed Captioned Video: Linear Functions: Negative Slope, Positive y-Intercept

Video Tutorial: Linear Functions: Negative Slope, Positive y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a positive y-intercept.

Graphs of Linear Functions
Closed Captioned Video: Linear Functions: Negative Slope, Zero y-Intercept Closed Captioned Video: Linear Functions: Negative Slope, Zero y-Intercept Closed Captioned Video: Linear Functions: Negative Slope, Zero y-Intercept

Video Tutorial: Linear Functions: Negative Slope, Zero y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a zero y-intercept.

Graphs of Linear Functions
Closed Captioned Video: Linear Functions: Positive Slope, Negative y-Intercept Closed Captioned Video: Linear Functions: Positive Slope, Negative y-Intercept Closed Captioned Video: Linear Functions: Positive Slope, Negative y-Intercept

Video Tutorial: Linear Functions: Positive Slope, Negative y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a negative y-intercept.

Graphs of Linear Functions
Closed Captioned Video: Linear Functions: Positive Slope, Positive y-Intercept Closed Captioned Video: Linear Functions: Positive Slope, Positive y-Intercept Closed Captioned Video: Linear Functions: Positive Slope, Positive y-Intercept

Video Tutorial: Linear Functions: Positive Slope, Positive y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a positive y-intercept.

Graphs of Linear Functions
Closed Captioned Video: Linear Functions: Positive Slope, Zero y-Intercept Closed Captioned Video: Linear Functions: Positive Slope, Zero y-Intercept Closed Captioned Video: Linear Functions: Positive Slope, Zero y-Intercept

Video Tutorial: Linear Functions: Positive Slope, Zero y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a zero y-intercept.

Graphs of Linear Functions
Definition--Linear Function Concepts--Constant Function Definition--Linear Function Concepts--Constant Function Constant Function

 

 

Topic

Linear Functions

Definition

A constant function is a linear function of the form f(x) = b, where b is a constant. The graph of a constant function is a horizontal line.

Description

Constant functions are a fundamental concept in linear functions. They represent scenarios where the output value remains unchanged, regardless of the input value. This is depicted graphically as a horizontal line, indicating that the function's rate of change is zero.

In real-world applications, constant functions can model situations where a quantity remains steady over time. For example, a flat fee service charge that does not vary with usage can be represented as a constant function.

Slope-Intercept Form
Definition--Linear Function Concepts--Converting from Standard Form to Slope-Intercept Form Definition--Linear Function Concepts--Converting from Standard Form to Slope-Intercept Form Converting from Standard Form to Slope-Intercept Form

 

 

Topic

Linear Functions

Definition

Converting from standard form to slope-intercept form involves rewriting a linear equation from the form Ax + By = C to the form y = mx + b, where m is the slope and b is the y-intercept.

Description

Converting linear equations from standard form to slope-intercept form is a key skill in algebra. This conversion allows for easier graphing and interpretation of the equation's slope and y-intercept.

Slope-Intercept Form
Definition--Linear Function Concepts--Decreasing Linear Function Definition--Linear Function Concepts--Decreasing Linear Function Decreasing Linear Function

 

 

Topic

Linear Functions

Definition

A decreasing linear function is a linear function where the slope is negative, indicating that as the input value increases, the output value decreases.

Description

Decreasing linear functions are important in understanding how variables inversely relate to each other. The negative slope signifies a reduction in the dependent variable as the independent variable increases.

Real-world examples include depreciation of assets over time or the decrease in temperature as altitude increases. These functions help model scenarios where an increase in one quantity results in a decrease in another.

Slope-Intercept Form
Definition--Linear Function Concepts--Direct Variation Definition--Linear Function Concepts--Direct Variation Direct Variation

 

 

Topic

Linear Functions

Definition

Direct 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.

Description

Direct variation is a fundamental concept in linear functions, illustrating how one variable changes proportionally with another. The constant of variation, 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.

Slope-Intercept Form
Definition--Linear Function Concepts--Equations of Parallel Lines Definition--Linear Function Concepts--Equations of Parallel Lines Equations of Parallel Lines

 

 

Topic

Linear Functions

Definition

Equations of parallel lines are linear equations that have the same slope but different y-intercepts, indicating that the lines never intersect.

Description

Understanding equations of parallel lines is crucial in geometry and algebra. Parallel lines have identical slopes, which means they run in the same direction and never meet.

In real-world applications, parallel lines can model scenarios such as railway tracks or lanes on a highway, where maintaining a consistent distance is essential.

Slope-Intercept Form
Definition--Linear Function Concepts--Equations of Perpendicular Lines Definition--Linear Function Concepts--Equations of Perpendicular Lines Equations of Perpendicular Lines

 

 

Topic

Linear Functions

Definition

Equations of perpendicular lines are linear equations where the slopes are negative reciprocals of each other, indicating that the lines intersect at a right angle.

Description

Equations of perpendicular lines are significant in both geometry and algebra. The negative reciprocal relationship between their slopes ensures that the lines intersect at a 90-degree angle.

In real-world applications, perpendicular lines are found in various structures, such as the intersection of streets or the corners of a building, where right angles are essential.

Slope-Intercept Form
Definition--Linear Function Concepts--Identity Function Definition--Linear Function Concepts--Identity Function Identity Function

 

 

Topic

Linear Functions

Definition

An identity function is a linear function of the form f(x) = x, where the output is equal to the input for all values of x.

Description

The identity function is a basic yet crucial concept in linear functions. It represents a scenario where the input value is always equal to the output value, graphically depicted as a 45-degree line passing through the origin.

In real-world applications, the identity function can model situations where input and output are directly proportional and identical, such as converting units of the same measure. This also introduces the concept of identity, which is fundamental to mathematics.

Slope-Intercept Form
Definition--Linear Function Concepts--Increasing Linear Function Definition--Linear Function Concepts--Increasing Linear Function Increasing Linear Function

 

 

Topic

Linear Functions

Definition

An increasing linear function is a linear function where the slope is positive, indicating that as the input value increases, the output value also increases.

Description

Increasing linear functions are essential in understanding how variables positively relate to each other. The positive slope signifies an increase in the dependent variable as the independent variable increases.

Real-world examples include income increasing with hours worked or the rise in temperature with the increase in daylight hours. These functions help model scenarios where an increase in one quantity results in an increase in another.

Slope-Intercept Form
Definition--Linear Function Concepts--Line of Best Fit Definition--Linear Function Concepts--Line of Best Fit Line of Best Fit

 

 

Topic

Linear Functions

Definition

A line of best fit is a straight line that best represents the data on a scatter plot, showing the trend of the data points.

Description

The line of best fit is a crucial concept in statistics and data analysis. It helps in identifying the trend and making predictions based on the data.

In real-world applications, the line of best fit is used in various fields such as economics, biology, and engineering to analyze trends and make forecasts. For example, it can be used to predict future sales based on past data.

Graphs of Linear Functions
Definition--Linear Function Concepts--Linear Equations in Standard Form Definition--Linear Function Concepts--Linear Equations in Standard Form Linear Equations in Standard Form

 

 

Topic

Linear Functions

Definition

Linear equations in standard form are written as Ax + By = C, where A, B, and C are constants, and A and B are not both zero.

Description

Linear equations in standard form are a fundamental representation of linear functions. They provide a way to express linear relationships in a general form.

Standard Form
Definition--Linear Function Concepts--Linear Function Definition--Linear Function Concepts--Linear Function Linear Function

 

 

Topic

Linear Functions

Definition

A linear function is a function that can be graphed as a straight line, typically written in the form y = mx + b, where m is the slope and b is the y-intercept.

Description

Linear functions are one of the most fundamental concepts in mathematics. They describe relationships where the rate of change between variables is constant, represented graphically as a straight line. This simplicity makes them a central topic in algebra and calculus.

Slope-Intercept Form
Definition--Linear Function Concepts--Linear Function Tables Definition--Linear Function Concepts--Linear Function Tables Linear Function Tables

 

 

Topic

Linear Functions

Definition

Linear function tables display the input-output pairs of a linear function, showing how the dependent variable changes with the independent variable.

Description

Linear 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--Linear Function Concepts--Point-Slope Form Definition--Linear Function Concepts--Point-Slope Form Point-Slope Form

 

 

Topic

Linear Functions

Definition

Point-slope form of a linear equation is written as y − y1 ​ = m(x−x1​ ), where m is the slope and (x1 ​ ,y1​) is a point on the line.

Description

The point-slope form is a versatile way to express linear equations, especially useful when you know a point on the line and the slope. It allows for quick construction of the equation of a line.

Point-Slope Form
Definition--Linear Function Concepts--Rate of Change Definition--Linear Function Concepts--Rate of Change Rate of Change

 

 

Topic

Linear Functions

Definition

Rate of change in a linear function is the ratio of the change in the dependent variable to the change in the independent variable, often represented as the slope m in the equation y = mx + b.

Description

Rate of change is a fundamental concept in understanding linear functions. It describes how one variable changes in relation to another, and is graphically represented by the slope of a line.

Slope
Definition--Linear Function Concepts--Slope-Intercept Form Definition--Linear Function Concepts--Slope-Intercept Form Slope-Intercept Form

 

 

Topic

Linear Functions

Definition

Slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Description

Slope-intercept form is one of the most commonly used forms of linear equations. It provides a clear way to understand the slope and y-intercept of a line, making it easier to graph and interpret.

In real-world applications, slope-intercept form is used in various fields such as economics, physics, and engineering to model linear relationships. For example, it can represent the relationship between cost and production levels in business.

Slope-Intercept Form
Definition--Linear Function Concepts--The Equation of a Line From Two Coordinates Definition--Linear Function Concepts--The Equation of a Line From Two Coordinates The Equation of a Line From Two Coordinates

 

 

Topic

Linear Functions

Definition

The equation of a line from two coordinates can be determined by finding the slope between the two points and using it in the point-slope form of a linear equation.

Description

Finding the equation of a line from two coordinates is a fundamental skill in algebra. It involves calculating the slope between the two points and then using one of the points to form the equation in point-slope or slope-intercept form.

Point-Slope Form
Definition--Linear Function Concepts--x-Intercept Definition--Linear Function Concepts--x-Intercept x-Intercept

 

 

Topic

Linear Functions

Definition

The x-intercept is the point where a graph crosses the x-axis, indicating the value of x when 𝑦 y is zero.

Description

The x-intercept is a key concept in understanding the behavior of linear functions. It represents the point where the function's output is zero, providing insight into the function's roots and behavior.

In real-world applications, the x-intercept can be used to determine break-even points in business, where revenue equals costs, or to find the time at which a process starts or stops.

Slope-Intercept Form
Definition--Linear Function Concepts--y-Intercept Definition--Linear Function Concepts--y-Intercept y-Intercept

 

 

Topic

Linear Functions

Definition

The y-intercept is the point where a graph crosses the y-axis, indicating the value of y when x is zero.

Description

The y-intercept is a fundamental concept in understanding the behavior of linear functions. It represents the initial value of the function when the input is zero, providing insight into the function's starting point.

In real-world applications, the y-intercept can be used to determine initial conditions in various scenarios, such as the starting balance in a bank account or the initial position of an object in motion.

Slope-Intercept Form
INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter 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
PowerPointPresentations.jpg 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 Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg 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 Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Cricket Chirps

In this Slide Show, apply concepts of linear functions to the context of cricket chirps.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Distance vs. Time

In this Slide Show, apply concepts of linear functions to the context of distance vs. time data and graphs.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg 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 Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions and Proportions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Momentum and Impulse

In this Slide Show, apply concepts of linear functions to the context of momentum and impulse.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Perimeter of a Rectangle

In this Slide Show, apply concepts of linear functions to the context of rectangular perimeter.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Saving Money

In this Slide Show, apply concepts of linear functions to the context of saving money.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Speed and acceleration

In this Slide Show, apply concepts of linear functions to the context of speed and acceleration.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions