Illustrative Math Alignment: Grade 8 Unit 3

This is the transcript that goes with the video segment entitled Video: Slope Formula: Positive Slope, Coordinates in Quadrants I and II.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video Tutorial: Slope Formula: Positive Slope, Coordinates in Quadrants III and IV.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Solving a System of Two Linear Equations.

To see the complete collection of video transcriptsy, click on this link.

Learn the basics of direct variations. Graphical and algebraic representations of direct variations are shown, as well as examples of such functions.

Topic

Linear Functions

Description

The video covers linear functions with positive slope and positive y-intercept. It explains the slope-intercept form y = mx + b, where m is the slope indicating steepness, calculated as rise over run, and b is the y-intercept, the y-value at the point where the line intersects the y-axis. For this function, the slope is 2, and the y-intercept is 2. The graph is demonstrated by moving up two units and one to the right, confirming the slope. The y-intercept at point (0, 2) is also identified.

Topic

Linear Functions

Description

This video discusses linear functions with positive slope and negative y-intercept. It reviews the slope-intercept form y = mx + b. The slope measures steepness as the ratio of rise to run, and the y-intercept is the point where the line meets the y-axis. Here, the slope is 2, and the y-intercept is -3, evidenced by the graph where the line starts at (0, -3) and rises two units for every unit right.

Topic

Linear Functions

Description

The video explains linear functions with a positive slope and zero y-intercept. In slope-intercept form y = mx + b, the slope, m, represents the steepness, while the y-intercept, b, is zero. The slope of 2 is confirmed by graphing: moving up two units and one to the right. The line passes through the origin, demonstrating a y-intercept of 0.

Topic

Linear Functions

Description

This video focuses on linear functions with a negative slope and positive y-intercept. Using the slope-intercept form y = mx + b, the slope of -3 indicates a downward slope, and the y-intercept of 2 is the point (0, 2). Graphically, moving down three units and one unit to the left confirms the slope of -3.

Topic

Linear Functions

Description

The video covers linear functions with a negative slope and negative y-intercept. It explains the slope-intercept form y = mx + b, with a slope of -3 and a y-intercept of -2 at (0, -2). The graph shows a downward slope with three units down and one unit left, confirming the slope.

Topic

Linear Functions

Description

This video addresses linear functions with a negative slope and zero y-intercept. In slope-intercept form y = mx + b, the slope is -3, indicating a downward trend. The line passes through the origin, confirming the zero y-intercept, and graphing demonstrates the negative slope.

In this video explore the relationship between slope and similar triangles.

Topic

Slope

Description

The video discusses a negative slope with points in Quadrants I and II. Using (4, 2) and (-2, 8), it calculates a slope of -1. Highlights include rise over run and coordinate simplifications.

This video illustrates the Slope, highlighting key mathematical concepts. Students will learn about the derivation and application of the slope formula through concrete examples and clear explanations. This lesson offers a foundational understanding crucial for graphing linear equations and interpreting real-world scenarios.

Topic

Slope

Description

This video demonstrates finding a positive slope with points in Quadrants III and IV. Using points (-5, -9) and (3, -5), it calculates a slope of 1/2. Concepts covered include rise over run and simplifying coordinate differences.

Topic

Slope

Description

Explains calculating a negative slope for points in Quadrants III and IV. Example points (7, -5) and (-5, -1) yield a slope of -1/3. Key topics include applying the slope formula and simplifying results.

This video illustrates the Slope, highlighting key mathematical concepts. Students will learn about the derivation and application of the slope formula through concrete examples and clear explanations. This lesson offers a foundational understanding crucial for graphing linear equations and interpreting real-world scenarios.

Topic

Slope

Description

The video covers finding a negative slope in Quadrant I using the slope formula. It defines rise over run and demonstrates calculations using points (7, 3) and (5, 7), resulting in a slope of -2. Important terms include numerator, denominator, and coordinates.

Topic

Slope

Description

This tutorial focuses on a positive slope in Quadrant II. Key topics include calculating slope as rise over run and using coordinate differences. It provides an example with points (-5, 4) and (-3, 8) resulting in a slope of 2. Vocabulary includes numerator, denominator, and difference.

Topic

Slope

Description

Explains finding a negative slope in Quadrant II using the slope formula. Demonstrates with points (-1, 4) and (-7, 6), resulting in a slope of -1/3. Covers key concepts like rise over run and coordinate differences.

Topic

Slope

Description

Shows how to calculate a positive slope in Quadrant III using the slope formula. Example uses points (-3, -8) and (-2, -2), with a slope of 6. Concepts include rise over run and simplifying fractions.

This video illustrates the Slope, highlighting key mathematical concepts. Students will learn about the derivation and application of the slope formula through concrete examples and clear explanations. This lesson offers a foundational understanding crucial for graphing linear equations and interpreting real-world scenarios.

Topic

Slope

Description

The video discusses finding a negative slope in Quadrant III using the slope formula. Points (-2, -7) and (-6, -5) result in a slope of -1/2. Highlights include simplifying coordinate differences and using the formula.

Topic

Slope

Description

Explains finding a positive slope in Quadrant IV. Demonstrates using points (2, -5) and (4, -1) to calculate a slope of 2. Vocabulary includes rise over run, numerator, and denominator.

This video illustrates the Slope, highlighting key mathematical concepts. Students will learn about the derivation and application of the slope formula through concrete examples and clear explanations. This lesson offers a foundational understanding crucial for graphing linear equations and interpreting real-world scenarios.

Topic

Slope

Description

Demonstrates calculating a negative slope in Quadrant IV. Example points are (9, -3) and (3, -1), with a slope of -1/3. Discusses coordinate differences and formula application.

This video illustrates the Slope, highlighting key mathematical concepts. Students will learn about the derivation and application of the slope formula through concrete examples and clear explanations. This lesson offers a foundational understanding crucial for graphing linear equations and interpreting real-world scenarios.

Topic

Slope

Description

Covers a positive slope with points spanning Quadrants I and II. Example uses (-3, 3) and (3, 6), yielding a slope of 1/2. Discusses rise over run, numerator, and denominator.

This video illustrates the Slope, highlighting key mathematical concepts. Students will learn about the derivation and application of the slope formula through concrete examples and clear explanations. This lesson offers a foundational understanding crucial for graphing linear equations and interpreting real-world scenarios.

Topic

Slope

Description

This video explains the slope formula and applies it to find the positive slope of a line where two points are in Quadrant I. Key concepts include rise over run and calculating differences in coordinates. The example uses points (2, 3) and (6, 7) with the slope calculated as 1. Vocabulary includes rise, run, numerator, and denominator.

This is part of a collection of video tutorials on using the point-slope form to find the equation of a line that passes through a given point. Each video is a step-by-step tutorial.

Note: The download is a PDF template for use in modeling the examples shown in the videos.

This is part of a collection of video tutorials on using the point-slope form to find the equation of a line that passes through a given point. Each video is a step-by-step tutorial.

Note: The download is a PDF template for use in modeling the examples shown in the videos.

This is part of a collection of video tutorials on using the point-slope form to find the equation of a line that passes through a given point. Each video is a step-by-step tutorial.

Note: The download is a PDF template for use in modeling the examples shown in the videos.

This is part of a collection of video tutorials on using the point-slope form to find the equation of a line that passes through a given point. Each video is a step-by-step tutorial.

Note: The download is a PDF template for use in modeling the examples shown in the videos.

In this video students learn about the different types of slope. This includes positive slope, negative slope, zero slope, and no slope. This video provides visualizations of these types of slopes without relying on the slope formula.

This video provides a step-by-step tutorial on using the slope formula. In this example the slope is positive. Note the download is a PDF that can used to demonstrate the step-by-step calculations.

This video provides a step-by-step tutorial on using the slope formula. In this example the slope is positive. Note the download is a PDF that can used to demonstrate the step-by-step calculations.

This video provides a step-by-step tutorial on using the slope formula. In this example the slope is zero. Note the download is a PDF that can used to demonstrate the step-by-step calculations.

This video provides a step-by-step tutorial on using the slope formula. In this example the slope is negative. Note the download is a PDF that can used to demonstrate the step-by-step calculations.

This video provides a step-by-step tutorial on using the slope formula. In this example the slope is undefined. Note the download is a PDF that can used to demonstrate the step-by-step calculations.

In this video students learn how to calculate the slope of a line, given two coordinates. This is done by measuring the rise and the run and is a precursor to learning to use the slope formula. The video also discusses positive and negative slopes.

Topic

Linear Functions

Description

Applies linear functions to cycling, calculating hill grades and distances using slope formulas and graphing.

Linear functions are fundamental in understanding mathematical relationships between two variables. The video demonstrates their application in real-life scenarios, enhancing comprehension of key concepts like slope, intercepts, and graphical representation. This foundational knowledge prepares students for more advanced mathematical topics.

Topic

Linear Functions

Topic

Linear Functions

Description

Introduces linear functions with examples like staircases, explaining slope, intercepts, and applications in real-world scenarios.

Linear functions are fundamental in understanding mathematical relationships between two variables. The video demonstrates their application in real-life scenarios, enhancing comprehension of key concepts like slope, intercepts, and graphical representation. This foundational knowledge prepares students for more advanced mathematical topics.

Topic

Linear Functions

Description

Uses linear regression to analyze US oil consumption trends, projecting future usage and potential impact of Alaskan oil production.

Linear functions are fundamental in understanding mathematical relationships between two variables. The video demonstrates their application in real-life scenarios, enhancing comprehension of key concepts like slope, intercepts, and graphical representation. This foundational knowledge prepares students for more advanced mathematical topics.

Topic

Linear Functions

Description

Models maximum heart rate during aerobic exercise with linear equations, creating exercise charts for various age groups.

Linear functions are fundamental in understanding relationships where one quantity depends linearly on another. This video provides clear examples and context that make the topic relevant and engaging. Linear equations often represent real-world scenarios, from economic trends to scientific measurements, helping students relate the math to everyday life.

Topic

Systems of Equations

Description

Description: Explores profit and loss through linear functions, focusing on break-even points and business profitability using TI-Nspire for visualizations.

Topic

Systems of Equations

Description

Description: Discusses encryption using linear systems, demonstrating substitution ciphers and matrix-based encoding for secure communication.

Topic

Systems of Equations

Description

Description: Analyzes ballistic missile interception through quadratic systems, graphing missile paths and their intersection as solutions to equations.

Topic

Functions and Relations

Description

This section defines relations and functions, emphasizing domain, range, and dependent versus independent variables. Using examples like USB flash drive pricing, it illustrates tabular, graphical, and mapping representations. Key concepts include ordered pairs, Cartesian plane, and scatter plots. The TI-Nspire is utilized to model relationships and introduce functional analysis.

Topic

Functions and Relations

Description

In this Math Lab explore domain-to-range mappings for functions and relations.

Relevance to the Topic: This video is an essential resource for understanding Functions and Relations. By exploring the concepts and examples in this video, students will gain insights into the practical applications and theoretical underpinnings of Functions and Relations. It builds a strong foundation for future learning.

Topic

Functions and Relations

Description

Building on the prior section, this video elaborates on function rules and notation, graphing diverse functions such as linear, quadratic, and step functions. Key terms include domain, range, and vertical line test. Applications highlight real-world uses like analyzing study hours and grades. Technology aids in demonstrating increasing and decreasing functions visually.

Topic

Functions and Relations

Description

In this Math Lab use toothpicks to create unit squares and square arrays. Explore the functional relationship between length of the side of the square and the total number of toothpicks.

Topic

Linear Functions

Description

This video explores linear functions, emphasizing their applications in motion contexts like airplane altitude. Key topics include slope, y-intercept, and function representation using tools like the TI-Nspire. Vocabulary includes linear function, slope-intercept form, and dependent variable. Applications include predicting motion scenarios.

Topic

Linear Functions

Description

In this Math Lab explore the slopes of staircases. Compare the slope of a staircase when walking it in a straight path and compare it to the slope of a staircase walked in a staggered path.

In this video, students explore the mathematical concept of linear functions, gaining a deeper understanding of its applications. The video emphasizes how this concept helps in problem-solving and real-world scenarios, bridging the gap between abstract mathematics and practical application.

Topic

Linear Functions

Description

This video applies linear functions to environmental data analysis, predicting carbon dioxide levels using regression models. Key terms include regression, scatter plot, and slope. Applications highlight global warming trends and their impact using predictive analytics.

Topic

Linear Functions

Description

In this Math Lab explore water pressure by comparing the height of a column of water and the length of the corresponding jet of water.

In this video, students explore the mathematical concept of linear functions, gaining a deeper understanding of its applications. The video emphasizes how this concept helps in problem-solving and real-world scenarios, bridging the gap between abstract mathematics and practical application.