Illustrative Math Alignment: Grade 8 Unit 3

In this set of Quizlet flash cards test understanding of linear functions.

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

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What Are Composite Functions?

Evaluate linear functions of the form f(x) = ax + b in this 20-flash card set. The values of a and b are in the range -10 to 10.

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

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To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Evaluate linear functions of the form f(x) = ax + b in this 20-flash card set. The values of a and b are in the range -10 to 10.

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

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Evaluate linear functions of the form f(x) = ax + b in this 20-flash card set. The values of a and b are in the range -10 to 10.

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

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Evaluate linear functions of the form f(x) = ax + b in this 20-flash card set. The values of a and b are in the range -10 to 10.

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

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Evaluate linear functions of the form f(x) = ax + b in this 20-flash card set. The values of a and b are in the range -10 to 10.

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

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Evaluate linear functions of the form f(x) = ax + b in this 20-flash card set. The values of a and b are in the range -10 to 10.

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

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Evaluate linear functions of the form f(x) = ax + b in this 20-flash card set. The values of a and b are in the range -10 to 10.

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

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Evaluate linear functions of the form f(x) = ax + b in this 20-flash card set. The values of a and b are in the range -10 to 10.

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

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Evaluate linear functions of the form f(x) = ax + b in this 20-flash card set. The values of a and b are in the range -10 to 10.

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

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Evaluate linear functions of the form f(x) = ax + b in this 20-flash card set. The values of a and b are in the range -10 to 10.

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

Related Resources

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

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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

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

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.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

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.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

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.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

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.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

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.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

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.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

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.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

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.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

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.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

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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Mastering linear equations is essential for success on the SAT Math test, where the Heart of Algebra category makes up approximately 35% of the exam. This comprehensive lesson guides students through solving linear equations, simplifying algebraic expressions, and understanding slope-intercept and point-slope form. Step-by-step examples help students learn how to graph equations, recognize parallel and perpendicular lines, and interpret slope and intercepts in real-world scenarios.

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.