Illustrative Math Alignment: Grade 8 Unit 3

Linear Relationships

Lesson 11: Equations of All Kinds of Lines

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Video Definition 30--Linear Function Concepts--Discrete Linear Functions	Video Definition 30--Linear Function Concepts--Discrete Linear Functions 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.	Special Functions
Video Definition 31--Linear Function Concepts--Graph of a Linear Function	Video Definition 31--Linear Function Concepts--Graph of a Linear Function 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.	Graphs of Linear Functions
Video Definition 31--Linear Function Concepts--Graph of a Linear Function	Video Definition 31--Linear Function Concepts--Graph of a Linear Function 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.	Graphs of Linear Functions
Video Definition 31--Linear Function Concepts--Graph of a Linear Function	Video Definition 31--Linear Function Concepts--Graph of a Linear Function 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.	Graphs of Linear Functions
Video Definition 31--Linear Function Concepts--Graph of a Linear Function	Video Definition 31--Linear Function Concepts--Graph of a Linear Function 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.	Graphs of Linear Functions
Video Definition 31--Linear Function Concepts--Graph of a Linear Function	Video Definition 31--Linear Function Concepts--Graph of a Linear Function 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.	Graphs of Linear Functions
Video Definition 31--Linear Function Concepts--Graph of a Linear Function	Video Definition 31--Linear Function Concepts--Graph of a Linear Function 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.	Graphs of Linear Functions
Video Definition 32--Linear Function Concepts--Linear Binomial	Video Definition 32--Linear Function Concepts--Linear Binomial 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.	Polynomial Expressions
Video Definition 32--Linear Function Concepts--Linear Binomial	Video Definition 32--Linear Function Concepts--Linear Binomial 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.	Polynomial Expressions
Video Definition 32--Linear Function Concepts--Linear Binomial	Video Definition 32--Linear Function Concepts--Linear Binomial 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.	Polynomial Expressions
Video Definition 32--Linear Function Concepts--Linear Binomial	Video Definition 32--Linear Function Concepts--Linear Binomial 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.	Polynomial Expressions
Video Definition 32--Linear Function Concepts--Linear Binomial	Video Definition 32--Linear Function Concepts--Linear Binomial 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.	Polynomial Expressions
Video Definition 32--Linear Function Concepts--Linear Binomial	Video Definition 32--Linear Function Concepts--Linear Binomial 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.	Polynomial Expressions
Video Definition 33--Linear Function Concepts--Coefficient of the Linear Term	Video Definition 33--Linear Function Concepts--Coefficient of the Linear Term 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.	Variable Expressions
Video Definition 33--Linear Function Concepts--Coefficient of the Linear Term	Video Definition 33--Linear Function Concepts--Coefficient of the Linear Term 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.	Variable Expressions
Video Definition 33--Linear Function Concepts--Coefficient of the Linear Term	Video Definition 33--Linear Function Concepts--Coefficient of the Linear Term 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.	Variable Expressions
Video Definition 33--Linear Function Concepts--Coefficient of the Linear Term	Video Definition 33--Linear Function Concepts--Coefficient of the Linear Term 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.	Variable Expressions
Video Definition 33--Linear Function Concepts--Coefficient of the Linear Term	Video Definition 33--Linear Function Concepts--Coefficient of the Linear Term 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.	Variable Expressions
Video Definition 33--Linear Function Concepts--Coefficient of the Linear Term	Video Definition 33--Linear Function Concepts--Coefficient of the Linear Term 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.	Variable Expressions
Video Definition 34--Linear Function Concepts--Constant Term	Video Definition 34--Linear Function Concepts--Constant Term 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.	Numerical Expressions
Video Definition 34--Linear Function Concepts--Constant Term	Video Definition 34--Linear Function Concepts--Constant Term 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.	Numerical Expressions
Video Definition 34--Linear Function Concepts--Constant Term	Video Definition 34--Linear Function Concepts--Constant Term 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.	Numerical Expressions
Video Definition 34--Linear Function Concepts--Constant Term	Video Definition 34--Linear Function Concepts--Constant Term 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.	Numerical Expressions
Video Definition 34--Linear Function Concepts--Constant Term	Video Definition 34--Linear Function Concepts--Constant Term 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.	Numerical Expressions
Video Definition 34--Linear Function Concepts--Constant Term	Video Definition 34--Linear Function Concepts--Constant Term 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.	Numerical Expressions
Video Definition 4--Linear Function Concepts--Decreasing Linear Function	Video Definition 4--Linear Function Concepts--Decreasing Linear Function 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.	Slope-Intercept Form
Video Definition 4--Linear Function Concepts--Decreasing Linear Function	Video Definition 4--Linear Function Concepts--Decreasing Linear Function 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.	Slope-Intercept Form
Video Definition 4--Linear Function Concepts--Decreasing Linear Function	Video Definition 4--Linear Function Concepts--Decreasing Linear Function 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.	Slope-Intercept Form
Video Definition 4--Linear Function Concepts--Decreasing Linear Function	Video Definition 4--Linear Function Concepts--Decreasing Linear Function 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.	Slope-Intercept Form
Video Definition 4--Linear Function Concepts--Decreasing Linear Function	Video Definition 4--Linear Function Concepts--Decreasing Linear Function 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.	Slope-Intercept Form
Video Definition 4--Linear Function Concepts--Decreasing Linear Function	Video Definition 4--Linear Function Concepts--Decreasing Linear Function 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.	Slope-Intercept Form
Video Definition 5--Linear Function Concepts--Identity Function	Video Definition 5--Linear Function Concepts--Identity Function 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.	Slope-Intercept Form
Video Definition 5--Linear Function Concepts--Identity Function	Video Definition 5--Linear Function Concepts--Identity Function 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.	Slope-Intercept Form
Video Definition 5--Linear Function Concepts--Identity Function	Video Definition 5--Linear Function Concepts--Identity Function 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.	Slope-Intercept Form
Video Definition 5--Linear Function Concepts--Identity Function	Video Definition 5--Linear Function Concepts--Identity Function 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.	Slope-Intercept Form
Video Definition 5--Linear Function Concepts--Identity Function	Video Definition 5--Linear Function Concepts--Identity Function 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.	Slope-Intercept Form
Video Definition 5--Linear Function Concepts--Identity Function	Video Definition 5--Linear Function Concepts--Identity Function 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.	Slope-Intercept Form
Video Definition 6--Linear Function Concepts--Slope-Intercept Form	Video Definition 6--Linear Function Concepts--Slope-Intercept Form 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.	Slope-Intercept Form
Video Definition 6--Linear Function Concepts--Slope-Intercept Form	Video Definition 6--Linear Function Concepts--Slope-Intercept Form 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.	Slope-Intercept Form
Video Definition 6--Linear Function Concepts--Slope-Intercept Form	Video Definition 6--Linear Function Concepts--Slope-Intercept Form 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.	Slope-Intercept Form

Illustrative Math Alignment: Grade 8 Unit 3

Linear Relationships

Lesson 11: Equations of All Kinds of Lines

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