Illustrative Math Alignment: Grade 8 Unit 3

Topic

Linear Functions

Description

The term is "Correlation Coefficient," defined as a numerical measure quantifying the strength and direction of the linear relationship between two variables, ranging from -1 to 1. A scatterplot and calculation examples are provided to illustrate this concept. This term connects linear functions to data analysis, showing how linear relationships are quantified in statistics.

Topic

Linear Functions

Description

The term is "Linear Expression," defined as an algebraic expression consisting of at least one term where the variable has an exponent of 1. Examples include x, 2x - 3, and -4x + 8. This term establishes the foundation of linear algebra by focusing on the simplest forms of linear relationships.

Topic

Linear Functions

Description

The term is "Inverse of a Linear Function," defined as the function f-1(x) such that its graph is the mirror image of f(x) across the line y = x. An example is f(x) = -3x + 3 and its inverse f-1(x) = -1/3 * x + 1. This term introduces the concept of function inverses, showing symmetry in linear functions.

Topic

Linear Functions

Description

The term is "Piecewise Linear Functions," defined as special functions composed of linear function segments. Examples include step functions and absolute value functions. This term extends the scope of linear functions to piecewise and segmented applications, showcasing broader versatility.

Topic

Linear Functions

Description

The term is "Increasing Linear Function," defined as a linear function with a positive slope. The graph of the function slants up from left to right, represented as y = mx + b with m > 0. This term complements the concept of decreasing linear functions by focusing on positive slope behavior.

Topic

Linear Functions

Description

The term is "Discrete Linear Functions," defined as discontinuous functions made up of linear function parts. Examples include step functions, illustrated with a piecewise graph. This term extends the concept of linearity to piecewise or segmented functions, bridging the gap between continuous and discrete representations.

Topic

Linear Functions

Description

The term is "Graphs of Linear Functions," defined as a linear function in slope-intercept form y = mx + b that crosses the y-axis at (0, b) and has a slope of m. An example graph shows f(x) = 4x + 3 crossing the y-axis at (0, 3). This term visualizes how linear functions are represented on a graph, providing insight into slope and y-intercept properties.

Topic

Linear Functions

Description

The term is "Linear Binomial," defined as a linear polynomial consisting of two terms. Examples include x + 1, -3x + 2, and (x + 2)(x - 2) = x^2 - 4, demonstrating how linear binomials can factor into higher-order polynomials. This term builds on linear expressions by focusing on binomial cases, important for algebraic manipulation.

Topic

Linear Functions

Description

The term is "Coefficient of the Linear Term," defined as the numerical factor of the variable in a linear expression, equation, or function. Examples provided include x + 3, where the coefficient is 1; y = -3x + 4, where the coefficient is -3; and 7x - 6 = 15, where the coefficient is 7. This term introduces the concept of coefficients in linear expressions, forming the foundation for understanding how variables scale in linear equations.

Topic

Linear Functions

Description

The term is "Constant Term," defined as the numerical term of a linear expression, equation, or function. Examples include x + 5, where the constant is 5; y = 5x + 2, where the constant is 2; and 3x - 2y = 10, where the constant is 10. This term explains the role of constants in linear equations, showing how they affect the y-intercept in graphing linear functions.

Topic

Linear Functions

Description

The term is "Decreasing Linear Function," defined as a linear function with a negative slope. The graph of the function slants down from left to right, represented as y = mx + b with m < 0. This term explores a specific behavior of linear functions, illustrating how slope affects the direction of a graph.

Topic

Linear Functions

Description

The term is "Identity Function," defined as a linear function of the form y = x, where input values equal the output values. The graph is a line of slope 1. This term explains the simplest linear function and its unique property where the input equals the output.

Topic

Linear Functions

Description

The term is "Slope-Intercept Form," defined as the equation of a linear function written in a form that easily identifies the slope (m) and y-intercept (b). Represented as y = mx + b. This term focuses on the most common representation of linear equations, simplifying analysis and graphing.

Topic

Linear Functions

Description

The term is "Linear Function Table," defined as an input-output table where the output values have a common difference. An example shows a table with x-values increasing by 1 and f(x)-values increasing by 2. This term ties numerical patterns to linear functions, highlighting their consistent rate of change.

Topic

Linear Functions

Description

The term is "Point-Slope Form," defined as a formula used to find the equation of a line in slope-intercept form for a given set of coordinates and slope. The formula is y - y1 = m(x - x1). This term provides a useful tool for transitioning between graph-based data and algebraic representations of linear functions.

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 entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 1: AX + By = C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: AX + By = C. 

The corresponding video is at this Link.

Note: The download is a PDF file.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 2: AX + By = -C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: AX + By = -C. 

The corresponding video is at this Link.

Note: The download is a PDF file.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 3: Ax - By = C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: AX - By = C. 

The corresponding video is at this Link.

Note: The download is a PDF file.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 4: -Ax + By = C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: -Ax + By = C.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 5: Ax - By = -C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: Ax - By = -C. 

The corresponding video is at this Link.

Note: The download is a PDF file.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 6: -Ax + By = -C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: -Ax + By = -C.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 7: -Ax - By = C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: -Ax - By = C.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 8:-Ax - By = -C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: -Ax - By = -C.

This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Addition Equations."

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

This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Addition Equations 2."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Division Equations."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Multiplication Equations."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Subtraction Equations."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Subtraction Equations 2."

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This is a video transcript for the video on solving quadratic equations. In this video, we work with this version of the quadratic equation: ax^2 + bx + c = 0.

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

This is a video transcript for the video on solving quadratic equations. In this video, we work with this version of the quadratic equation: ax^2 + bx - c = 0.

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

This is a video transcript for the video on solving quadratic equations. In this video, we work with this version of the quadratic equation: ax^2 - bx + c = 0.

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

This is a video transcript for the video on solving quadratic equations. In this video, we work with this version of the quadratic equation: -ax^2 + bx + c = 0.

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

This is a video transcript for the video on solving quadratic equations. In this video, we work with this version of the quadratic equation: ax^2 - bx - c = 0.

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

This is a video transcript for the video on solving quadratic equations. In this video, we work with this version of the quadratic equation: -ax^2 + bx - c = 0.

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

This is a video transcript for the video on solving quadratic equations. In this video, we work with this version of the quadratic equation: -ax^2 - bx + c = 0.

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

This is a video transcript for the video on solving quadratic equations. In this video, we work with this version of the quadratic equation: -ax^2 - bx - c = 0.

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

This is the transcript for the video entitled, Anatomy of an Equation: Two-Step Equations 1. In this video learn the mechanics of solving a two-step equation involving addition and multiplication.

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

This is the transcript for the video entitled, Anatomy of an Equation: Two-Step Equations 10. In this video learn the mechanics of solving a two-step equation involving addition and division. In this variation, the x-term has a negative coefficient.

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

This is the transcript for the video entitled, Anatomy of an Equation: Two-Step Equations 11. In this video learn the mechanics of solving a two-step equation involving addition and division. In this variation, the x-term has a negative coefficient. In this variation, the term on the other side of the equals sign is negative.

This is the transcript for the video entitled, Anatomy of an Equation: Two-Step Equations 12. In this video learn the mechanics of solving a two-step equation involving subtraction and division.

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

This is the transcript for the video entitled, Anatomy of an Equation: Two-Step Equations 13. In this video learn the mechanics of solving a two-step equation involving subtraction and division. In this variation, the x-term has a negative coefficient. In this variation, the term on the other side of the equals sign is negative.

This is the transcript for the video entitled, Anatomy of an Equation: Two-Step Equations 2. In this video learn the mechanics of solving a two-step equation involving addition and multiplication. In this variation, the term on the other side of the equals sign is negative.

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

This is the transcript for the video entitled, Anatomy of an Equation: Two-Step Equations 3. In this video learn the mechanics of solving a two-step equation involving subtraction and multiplication.

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

This is the transcript for the video entitled, Anatomy of an Equation: Two-Step Equations 4. In this video learn the mechanics of solving a two-step equation involving subtraction and multiplication. In this variation, the number on the other side of the equals sign is negative.

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

This is the transcript for the video entitled, Anatomy of an Equation: Two-Step Equations 5. In this video learn the mechanics of solving a two-step equation involving addition and multiplication. In this variation, the x-term has a negative coefficient.

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

This is the transcript for the video entitled, Anatomy of an Equation: Two-Step Equations 6. In this video learn the mechanics of solving a two-step equation involving addition and multiplication. In this variation, the x-term has a negative coefficient and the term on the other side of the equals sign is negative.

This is the transcript for the video entitled, Anatomy of an Equation: Two-Step Equations 7. In this video learn the mechanics of solving a two-step equation involving subtraction and multiplication. In this variation, the x-term has a negative coefficient.

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

This is the transcript for the video entitled, Anatomy of an Equation: Two-Step Equations 8. In this video learn the mechanics of solving a two-step equation involving subtraction and multiplication. In this variation, the x-term has a negative coefficient and the term on the other side of the equals sign is negative.