Illustrative Math Alignment: Grade 8 Unit 3

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.

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.

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.

Video Tutorial: Slope Formula: Negative Slope, Coordinates in Quadrant I. In this tutorial, students learn about the slope formula in general and then see an application of it with two points in Quadrant I.

This is part of a collection of video tutorials on the topic of the Slope Formula. These videos cover ways of calculating slope, as well as positive, negative, zero, and undefined slope.

Video Tutorial: Slope Formula: Negative Slope, Coordinates in Quadrant II. In this tutorial, students learn about the slope formula in general and then see an application of it with two points in Quadrant II.

This is part of a collection of video tutorials on the topic of the Slope Formula. These videos cover ways of calculating slope, as well as positive, negative, zero, and undefined slope.

Video Tutorial: Slope Formula: Negative Slope, Coordinates in Quadrant III. In this tutorial, students learn about the slope formula in general and then see an application of it with two points in Quadrant III.

This is part of a collection of video tutorials on the topic of the Slope Formula. These videos cover ways of calculating slope, as well as positive, negative, zero, and undefined slope.

Video Tutorial: Slope Formula: Negative Slope, Coordinates in Quadrant IV. In this tutorial, students learn about the slope formula in general and then see an application of it with two points in Quadrant IV.

This is part of a collection of video tutorials on the topic of the Slope Formula. These videos cover ways of calculating slope, as well as positive, negative, zero, and undefined slope.

Video Tutorial: Slope Formula: Negative Slope, Coordinates in Quadrants I and II. In this tutorial, students learn about the slope formula in general and then see an application of it with two points in Quadrant I and Quadrant II.

This is part of a collection of video tutorials on the topic of the Slope Formula. These videos cover ways of calculating slope, as well as positive, negative, zero, and undefined slope.

Video Tutorial: Slope Formula: Negative Slope, Coordinates in Quadrants III and IV. In this tutorial, students learn about the slope formula in general and then see an application of it with two points in Quadrant III and Quadrant IV.

This is part of a collection of video tutorials on the topic of the Slope Formula. These videos cover ways of calculating slope, as well as positive, negative, zero, and undefined slope.

Video Tutorial: Slope Formula: Positive Slope, Coordinates in Quadrant I. In this tutorial, students learn about the slope formula in general and then see an application of it with two points in Quadrant I.

This is part of a collection of video tutorials on the topic of the Slope Formula. These videos cover ways of calculating slope, as well as positive, negative, zero, and undefined slope.

Video Tutorial: Slope Formula: Positive Slope, Coordinates in Quadrant II. In this tutorial, students learn about the slope formula in general and then see an application of it with two points in Quadrant II.

This is part of a collection of video tutorials on the topic of the Slope Formula. These videos cover ways of calculating slope, as well as positive, negative, zero, and undefined slope.

Video Tutorial: Slope Formula: Positive Slope, Coordinates in Quadrant III. In this tutorial, students learn about the slope formula in general and then see an application of it with two points in Quadrant III.

This is part of a collection of video tutorials on the topic of the Slope Formula. These videos cover ways of calculating slope, as well as positive, negative, zero, and undefined slope.

Video Tutorial: Slope Formula: Positive Slope, Coordinates in Quadrant IV. In this tutorial, students learn about the slope formula in general and then see an application of it with two points in Quadrant IV.

This is part of a collection of video tutorials on the topic of the Slope Formula. These videos cover ways of calculating slope, as well as positive, negative, zero, and undefined slope.

Video Tutorial: Slope Formula: Positive Slope, Coordinates in Quadrants I and II. In this tutorial, students learn about the slope formula in general and then see an application of it with two points in Quadrant I and Quadrant II.

This is part of a collection of video tutorials on the topic of the Slope Formula. These videos cover ways of calculating slope, as well as positive, negative, zero, and undefined slope.

Video Tutorial: Slope Formula: Positive Slope, Coordinates in Quadrants III and IV. In this tutorial, students learn about the slope formula in general and then see an application of it with two points in Quadrant III and Quadrant IV.

This is part of a collection of video tutorials on the topic of the Slope Formula. These videos cover ways of calculating slope, as well as positive, negative, zero, and undefined slope.

In this TI Nspire tutorial for the TI-Nspire CAS, the Calculator Window is used to solve a linear system. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

Related Resources

Video Transcripts

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 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.

Topic

Slope

Definition

Delta x is the change in the x-coordinate in a linear relationship.

Description

The term Delta x is fundamental to understanding slope as it represents the horizontal change in a line’s position. In real-world applications, Delta x can represent the distance traveled over time in physics and engineering contexts.

Topic

Slope

Definition

Delta y is the change in the y-coordinate in a linear relationship.

Description

The term Delta y signifies the vertical change, essential for calculating slope used in graphing and data interpretation. In practical scenarios, Delta y can illustrate changes in temperature over time or the rise in elevation in geography.

Topic

Slope

Definition

Grade is a ratio indicating the steepness of a slope.

Description

The term Grade commonly refers to the angle of elevation or slope expressed as a percentage. In engineering, grades are crucial for designing roads and railways, ensuring safety and efficiency.

Topic

Slope

Definition

Gradient represents the rate of change of a quantity.

Description

The Gradient measures how steep a line is, calculated by the ratio of the rise to run. This concept is significant in fields like physics and economics where gradients can represent relationships between variables.

Topic

Slope

Definition

Negative Slope indicates a decrease in value as x increases.

Description

The Negative Slope signifies that as one variable increases, the other decreases, often used in economics to depict inverse relationships. This term finds relevance in real-world scenarios like demand curves which slope downwards.

Topic

Slope

Definition

Pitch refers to the steepness of a slope in a real-world context.

Description

Pitch is commonly applied in construction and design fields to denote the angle of roofs and ramps. This is essential in architecture, especially when dealing with drainage and material use.

Topic

Slope

Definition

Point-Slope Form is a way to express linear equations given the slope and a point on the line.

Description

The Point-Slope Form is crucial in algebra for identifying linear relationships given the slope and a point on the line. Understanding this concept aids in graphing lines efficiently and is foundational in higher mathematics.

For a complete collection of terms related to Slope click on this link: Slope Collection.

Topic

Slope

Definition

Positive Slope indicates an increase in value as x increases.

Description

The Positive Slope indicates that as x grows, y also rises, signifying direct relationships in data analysis. This principle enables predictions in various analytics and trends.

For a complete collection of terms related to Slope click on this link: Slope Collection.

Topic

Slope

Definition

Slope measures the steepness of a line.

Description

Slope is a fundamental concept in mathematics, expressing the ratio of vertical rise to horizontal run. This is vital for understanding linear functions, essential in fields such as physics, economics, and data science.

For a complete collection of terms related to Slope click on this link: Slope Collection.

Topic

Slope

Definition

The Slope Formula calculates the rate of change.

Description

The Slope Formula is typically represented as 

This formula is a cornerstone in algebra, enabling students to analyze linear equations effectively.

Topic

Slope

Definition

The slope-intercept form is an equation of a straight line represented as y = m x + b, where m is the slope and b is the y-intercept.

Description

The slope-intercept form is a fundamental concept in algebra, providing a straightforward way to graph linear equations. It is widely used in various fields, from economics to physics, to model linear relationships and predict outcomes based on given data. Understanding this form is crucial for students as it lays the foundation for more complex mathematical concepts and real-world applications.

Topic

Slope

Definition

Parallel lines are lines in the same plane that never meet; they have equal slopes.

Description

Understanding the slopes of parallel lines is essential in geometry and algebra, as it helps in identifying and proving parallelism in shapes and graphs. This concept is applied in various fields, including architecture and engineering, where maintaining parallelism is crucial for structural integrity and design. In mathematics education, this concept aids in developing logical reasoning and problem-solving skills.

Topic

Slope

Definition

Perpendicular lines intersect at a right angle, and their slopes are negative reciprocals of each other.

Description

The concept of perpendicular slopes is vital in geometry, as it helps in determining the orthogonality of lines. This principle is used in various applications, such as designing perpendicular intersections in roadways and creating right-angle joints in construction. In education, it enhances students' understanding of geometric properties and their ability to solve related problems.

Topic

Slope

Definition

Steepness is a measure of how steep a line is, typically calculated as the absolute value of the slope.

Description

Steepness is a key concept in understanding the inclination of lines and surfaces. It is commonly used in fields like geology and civil engineering to assess the gradient of terrains and structures. In math education, learning about steepness helps students grasp the concept of slope and its practical implications, enhancing their analytical skills and understanding of real-world phenomena.

Topic

Slope

Definition

The rise over the run describes the change in y over the change in x in a linear relationship.

Description

The concept of "rise over run" is foundational in understanding how to calculate the slope of a line. It is used in various disciplines, such as physics and economics, to model relationships and predict trends. In education, mastering this concept is crucial for students as it forms the basis for graphing linear equations and understanding the behavior of lines in a coordinate plane.

Topic

Slope

Definition

Undefined slope occurs when a vertical line is present, meaning there is no change in x.

Description

An undefined slope is a critical concept in mathematics, particularly in graphing. It indicates a vertical line where the change in x is zero, making the slope calculation impossible. This concept is important in various fields, such as computer graphics and data analysis, where vertical lines can represent boundaries or limits. Understanding undefined slopes helps students in identifying and interpreting vertical lines in graphs.

Topic

Slope

Definition

Zero slope describes a horizontal line where there is no change in y as x changes.

Description

A zero slope is a key concept in algebra and geometry, representing a horizontal line. It is used in various applications, such as designing flat surfaces and analyzing constant relationships in data. In education, understanding zero slopes helps students in graphing and interpreting horizontal lines, enhancing their ability to analyze linear relationships.

For a complete collection of terms related to Slope click on this link: Slope Collection.

This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems.

This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems.

This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems.

This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems.

This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems.

This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems.

This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems.

In this graphing calculator activity, have your students explore how to convert linear equations in standard form to a linear function in slope-intercept form. This Desmos template allows students to explore the effect of changes in the values of A, B, and C in the standard form and m and b in the slope-intercept form. A companion downloadable worksheet uses the graphing calculator template to explore the properties of these linear equations and functions. Note: The download is a PDF worksheet.

The following section includes background information on slope. This background also includes video resources and accompanying transcripts.

Use this activity to explore slope as a rate of change. In this Desmos activity, the slope of the line is the rate (cost per pound) for purchasing fruit. Students manipulate the slider for m to see the impact on the cost.

This Desmos activity allows students to explore slope as the ratio of the rise over the run. Click Preview to launch the activity. In the activity students click on the points to create a line segment connecting two points. Use the background grid to determine the rise and the run and calculate the slope.

Desmos Activity: Slope As Rise Over Run 2

In this activity, students input different values for the coordinates to create a new line. They can then measure the rise and run to calculate the slope.

The formula for the Slope Formula. This is part of a collection of math formulas. 

The following section includes background information on slope. This background also includes video resources and accompanying transcripts.

What Is Slope?

Watch this video to learn about the slope formula. (The transcript is also included.)

Learn different strategies for finding the slope of a line. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems.

Note: The download is a PPT file.

In this Slide Show, use the Desmos graphing calculator to explore the point-slope form. To see the complete collection of Desmos Resources click on this link.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

The complete set of 13 examples that make up this set of tutorials.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

The complete set of 29 examples that make up this set of tutorials.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.