Illustrative Math Alignment: Grade 8 Unit 3

In this set of interactive flash cards, find the inverse of a given linear function.

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In this set of interactive flash cards, find the inverse of a given linear function.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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

Quizlet Library

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In this set of Quizlet flash cards test understanding of the point-slope form.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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In this set of Quizlet flash cards test understanding of the slope-intercept form.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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This is part of a collection of self-scoring interactive math quizzes on a variety of topics.

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In this TI-84 tutorial we show how to graph linear functions and trace their coordinates. Note: The download is a PPT file.

Topic

Linear Functions

Description

The term is "Linear Function," defined as a function of the form y = mx + b, where m is the slope of the line and b is the y-intercept. This term provides the basic definition of linear functions, integral to understanding their behavior and applications.

Topic

Linear Functions

Description

The term is "y-Intercept," defined as the point on the y-axis where a linear function intersects. In slope-intercept form, it is designated as b in y = mx + b. This term complements the x-intercept by focusing on the vertical axis, completing the understanding of graph interactions.

Topic

Linear Functions

Description

The term is "x-Intercept," defined as the point on the x-axis where a linear function intersects, calculated as x = -b/m when y = 0 in the equation y = mx + b. This term provides insight into the graphical representation of linear functions and their interaction with the x-axis.

Topic

Linear Functions

Description

The term is "Rate of Change," defined as the slope, interpreted as the rate at which the dependent variable changes relative to the independent variable. An example is speed as a rate of change of distance over time. This term highlights the application of slope in real-world scenarios, making the concept more tangible and relatable.

Topic

Linear Functions

Description

The term is "Equations of Perpendicular Lines," defined as two linear functions with graphs that are perpendicular. Their slopes are negative reciprocals, represented as y1 = mx + b1 and y2 = -1/m * x + b2. This term explores the relationship between slopes of perpendicular lines, deepening understanding of linear graph orientations.

Topic

Linear Functions

Description

The term is "Equations of Parallel Lines," defined as two linear functions with parallel graphs that have the same slope but different y-intercepts. Represented as y1 = mx + b1 and y2 = mx + b2, where m is the slope. This term explains the geometric relationship of parallel lines, reinforcing the role of slope in linear functions.

Topic

Linear Functions

Description

The term is "Linear Equation in Standard Form," defined as a linear equation with two variables and three constant terms, represented as Ax + By = C where A and B are not equal to zero. This term sets the stage for converting between forms of linear equations, essential for solving and graphing.

Topic

Linear Functions

Description

The term is "Converting from Standard Form to Slope-Intercept Form," defined as rewriting a linear equation in the form y = mx + b using the constants from the standard form Ax + By = C. The conversion formula is y = -A/B * x + C/B. This term is crucial for transitioning between different representations of linear equations, enabling easier analysis and graphing.

Topic

Linear Functions

Description

The term is "Direct Variation," defined as a linear function of the form y = kx, where k is the constant of variation. Graphs of direct variations cross the origin, and the constant of variation is the slope of the graph. This term emphasizes proportional relationships in linear functions, highlighting their simplicity and graphical characteristics.

Topic

Linear Functions

Description

The term is "Line of Best Fit," defined as a linear function that serves as a model for a set of scatterplot data. It helps represent the central trend of data points. This term enhances understanding of linear functions in the context of data analysis and graphical trends.

Topic

Linear Functions

Description

The term is "Slope of a Line," defined as the ratio of the rise over the run, or the change in vertical distance over the change in horizontal distance. Represented as m in the equation y = mx + b. This term is a fundamental component of linear equations, providing a measure of steepness and direction.

Topic

Linear Functions

Description

The term is "Constant Function," defined as a linear function of the form y = b, where b is the y-intercept. The graph of a constant function is horizontal with a slope of m = 0. An example graph is shown with a horizontal line at y = b. This term demonstrates a special case of linear functions, emphasizing the role of constant values and their graphical representation as horizontal lines.

Topic

Linear Functions

Description

The term is "System of Linear Equations," defined as a collection of linear equations where the number of equations matches the number of variables, allowing for an algebraic solution. Examples include 2-variable and 3-variable systems. This term introduces the concept of interacting linear equations, paving the way for multi-variable problem-solving.

Topic

Linear Functions

Description

The term is "Solution to a Linear Equation," defined as finding the value(s) of a variable that make the equation true. An example includes solving 2x + 5 = 15 step-by-step to find x = 5. This term explains how linear equations are solved, demonstrating the logical process of isolating variables.

Topic

Linear Functions

Description

The term is "Proportional Relationship," defined as a type of linear relationship where two variables maintain a constant ratio. Represented as y = kx, where k is the constant ratio. This term establishes the foundation for understanding direct variation and proportionality in linear relationships.

Topic

Linear Functions

Description

The term is "Scatter Plot," defined as a graph displaying individual data points as dots, where each dot represents the values of two variables. Used to examine relationships and identify patterns or trends. This term provides a graphical tool to visualize and analyze linear relationships in data.

Topic

Linear Functions

Description

The term is "Least Squares Regression Line," defined as the best fit to a set of data points on a scatter plot. It minimizes the sum of the squares of the vertical distances between the data points and the line. This term links linear functions to data analysis, providing a method to model relationships in data.

Topic

Linear Functions

Description

The term is "Linear Regression," defined as a statistical method used to analyze the relationship between two variables by fitting a linear equation to observed data points. An example includes using LinReg to calculate slope (m), intercept (b), and r-squared values. This term links linear functions with statistical applications, particularly in modeling and predictions based on data.

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.

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

This is the transcript for the video of same title. Video contents: 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

This is the transcript for the video of same title. Video contents: In this Investigation we explore the definition of a Relation.

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This is the transcript for the video of same title. Video contents: In this Investigation we look at functions.

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

This is the transcript for the video of same title. Video contents: 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

This is the transcript for the video of same title. Video contents: In this Investigation we look at linear models for objects moving at a constant speed.

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