Illustrative Math Alignment: Grade 8 Unit 2

Topic

Linear Functions

Description

The term is "The Equation of a Line from Two Coordinates," defined as deriving the equation of a line in slope-intercept form from two given points. The slope is calculated as m = (y2 - y1) / (x2 - x1), and the equation is written as y - y1 = m(x - x1). This term builds the connection between points on a graph and their corresponding linear equation, demonstrating practical derivations.

This is the transcript for the video of same title. Video contents: In this program we look at applications of transformations. We do this in the context of three real-world applications. In the first, we look at translations and rotations in the context of roller coaster rides. In the second example we look at translations in three-dimensional space in the context of cargo ships. In the third example, we look at the design of observatories to look at rotations, reflections, and symmetry.

This is the transcript for the video of same title. Video contents: Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced.

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This is the transcript for the video of same title. Video contents: Cargo ships transport tons of merchandise from one country to another and accounts for most of the global economy. Loading and unloading these ships requires a great deal of organization and provides an ideal example of three-dimensional translations.

This is the transcript for the video of same title. Video contents: The Gemini telescope in Hawaii is an example of architecture that moves. All observatories rotate in order to follow objects in the sky. This also provides an opportunity to explore rotations, reflections, and symmetry.

This is the transcript that goes with the video segment entitled Video: Linear Functions: Negative Slope, Negative y-Intercept.

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This is the transcript that goes with the video segment entitled Video: Linear Functions: Negative Slope, Positive y-Intercept.

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This is the transcript that goes with the video segment entitled Video: Linear Functions: Negative Slope, Zero y-Intercept.

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This is the transcript that goes with the video segment entitled Video: Linear Functions: Positive Slope, Negative y-Intercept.

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This is the transcript that goes with the video segment entitled Video: Linear Functions: Positive Slope, Positive y-Intercept.

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This is the transcript that goes with the video segment entitled Video: Linear Functions: Positive Slope, Zero y-Intercept.

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This is the transcript that goes with the video segment entitled Video Tutorial: Slope Formula: Negative Slope, Coordinates in Quadrant I.

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This is the transcript that goes with the video segment entitled Video Tutorial: Slope Formula: Negative Slope, Coordinates in Quadrant II.

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This is the transcript that goes with the video segment entitled Video Tutorial: Negative Slope, Coordinates in Quadrant III.

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This is the transcript that goes with the video segment entitled Video Tutorial: Slope Formula: Negative Slope, Coordinates in Quadrant IV.

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

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

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

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

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

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

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

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

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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.

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

Transformations