Illustrative Math Alignment: Grade 8 Unit 6

Topic

Linear Functions

Definition

An increasing linear function is a linear function where the slope is positive, indicating that as the input value increases, the output value also increases.

Description

Increasing linear functions are essential in understanding how variables positively relate to each other. The positive slope signifies an increase in the dependent variable as the independent variable increases.

Real-world examples include income increasing with hours worked or the rise in temperature with the increase in daylight hours. These functions help model scenarios where an increase in one quantity results in an increase in another.

Topic

Linear Functions

Definition

A line of best fit is a straight line that best represents the data on a scatter plot, showing the trend of the data points.

Description

The line of best fit is a crucial concept in statistics and data analysis. It helps in identifying the trend and making predictions based on the data.

In real-world applications, the line of best fit is used in various fields such as economics, biology, and engineering to analyze trends and make forecasts. For example, it can be used to predict future sales based on past data.

Topic

Linear Functions

Definition

A line of best fit is a straight line that best represents the data on a scatter plot, showing the trend of the data points.

Description

The line of best fit is a crucial concept in statistics and data analysis. It helps in identifying the trend and making predictions based on the data.

In real-world applications, the line of best fit is used in various fields such as economics, biology, and engineering to analyze trends and make forecasts. For example, it can be used to predict future sales based on past data.

Topic

Linear Functions

Definition

A line of best fit is a straight line that best represents the data on a scatter plot, showing the trend of the data points.

Description

The line of best fit is a crucial concept in statistics and data analysis. It helps in identifying the trend and making predictions based on the data.

In real-world applications, the line of best fit is used in various fields such as economics, biology, and engineering to analyze trends and make forecasts. For example, it can be used to predict future sales based on past data.

Topic

Linear Functions

Definition

Linear equations in standard form are written as Ax + By = C, where A, B, and C are constants, and A and B are not both zero.

Description

Linear equations in standard form are a fundamental representation of linear functions. They provide a way to express linear relationships in a general form.

Topic

Linear Functions

Definition

Linear equations in standard form are written as Ax + By = C, where A, B, and C are constants, and A and B are not both zero.

Description

Linear equations in standard form are a fundamental representation of linear functions. They provide a way to express linear relationships in a general form.

Topic

Linear Functions

Definition

Linear equations in standard form are written as Ax + By = C, where A, B, and C are constants, and A and B are not both zero.

Description

Linear equations in standard form are a fundamental representation of linear functions. They provide a way to express linear relationships in a general form.

Topic

Linear Functions

Definition

A linear function is a function that can be graphed as a straight line, typically written in the form y = mx + b, where m is the slope and b is the y-intercept.

Description

Linear functions are one of the most fundamental concepts in mathematics. They describe relationships where the rate of change between variables is constant, represented graphically as a straight line. This simplicity makes them a central topic in algebra and calculus.

Topic

Linear Functions

Definition

A linear function is a function that can be graphed as a straight line, typically written in the form y = mx + b, where m is the slope and b is the y-intercept.

Description

Linear functions are one of the most fundamental concepts in mathematics. They describe relationships where the rate of change between variables is constant, represented graphically as a straight line. This simplicity makes them a central topic in algebra and calculus.

Topic

Linear Functions

Definition

A linear function is a function that can be graphed as a straight line, typically written in the form y = mx + b, where m is the slope and b is the y-intercept.

Description

Linear functions are one of the most fundamental concepts in mathematics. They describe relationships where the rate of change between variables is constant, represented graphically as a straight line. This simplicity makes them a central topic in algebra and calculus.

Topic

Linear Functions

Definition

Linear function tables display the input-output pairs of a linear function, showing how the dependent variable changes with the independent variable.

Description

Linear function tables are useful tools for understanding and analyzing linear relationships. They provide a clear way to see how changes in the input (independent variable) affect the output (dependent variable).

Topic

Linear Functions

Definition

Linear function tables display the input-output pairs of a linear function, showing how the dependent variable changes with the independent variable.

Description

Linear function tables are useful tools for understanding and analyzing linear relationships. They provide a clear way to see how changes in the input (independent variable) affect the output (dependent variable).

Topic

Linear Functions

Definition

Linear function tables display the input-output pairs of a linear function, showing how the dependent variable changes with the independent variable.

Description

Linear function tables are useful tools for understanding and analyzing linear relationships. They provide a clear way to see how changes in the input (independent variable) affect the output (dependent variable).

Topic

Linear Functions

Definition

Linear function tables display the input-output pairs of a linear function, showing how the dependent variable changes with the independent variable.

Description

Linear function tables are useful tools for understanding and analyzing linear relationships. They provide a clear way to see how changes in the input (independent variable) affect the output (dependent variable).

Topic

Linear Functions

Definition

Point-slope form of a linear equation is written as y − y1 ​ = m(x−x1​ ), where m is the slope and (x1 ​ ,y1​) is a point on the line.

Description

The point-slope form is a versatile way to express linear equations, especially useful when you know a point on the line and the slope. It allows for quick construction of the equation of a line.

Topic

Linear Functions

Definition

Point-slope form of a linear equation is written as y − y1 ​ = m(x−x1​ ), where m is the slope and (x1 ​ ,y1​) is a point on the line.

Description

The point-slope form is a versatile way to express linear equations, especially useful when you know a point on the line and the slope. It allows for quick construction of the equation of a line.

Topic

Linear Functions

Definition

Point-slope form of a linear equation is written as y − y1 ​ = m(x−x1​ ), where m is the slope and (x1 ​ ,y1​) is a point on the line.

Description

The point-slope form is a versatile way to express linear equations, especially useful when you know a point on the line and the slope. It allows for quick construction of the equation of a line.

Topic

Linear Functions

Definition

Point-slope form of a linear equation is written as y − y1 ​ = m(x−x1​ ), where m is the slope and (x1 ​ ,y1​) is a point on the line.

Description

The point-slope form is a versatile way to express linear equations, especially useful when you know a point on the line and the slope. It allows for quick construction of the equation of a line.

Topic

Linear Functions

Definition

Rate of change in a linear function is the ratio of the change in the dependent variable to the change in the independent variable, often represented as the slope m in the equation y = mx + b.

Description

Rate of change is a fundamental concept in understanding linear functions. It describes how one variable changes in relation to another, and is graphically represented by the slope of a line.

Topic

Linear Functions

Definition

Rate of change in a linear function is the ratio of the change in the dependent variable to the change in the independent variable, often represented as the slope m in the equation y = mx + b.

Description

Rate of change is a fundamental concept in understanding linear functions. It describes how one variable changes in relation to another, and is graphically represented by the slope of a line.

Topic

Linear Functions

Definition

Rate of change in a linear function is the ratio of the change in the dependent variable to the change in the independent variable, often represented as the slope m in the equation y = mx + b.

Description

Rate of change is a fundamental concept in understanding linear functions. It describes how one variable changes in relation to another, and is graphically represented by the slope of a line.

Topic

Linear Functions

Definition

Slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Description

Slope-intercept form is one of the most commonly used forms of linear equations. It provides a clear way to understand the slope and y-intercept of a line, making it easier to graph and interpret.

In real-world applications, slope-intercept form is used in various fields such as economics, physics, and engineering to model linear relationships. For example, it can represent the relationship between cost and production levels in business.

Topic

Linear Functions

Definition

Slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Description

Slope-intercept form is one of the most commonly used forms of linear equations. It provides a clear way to understand the slope and y-intercept of a line, making it easier to graph and interpret.

In real-world applications, slope-intercept form is used in various fields such as economics, physics, and engineering to model linear relationships. For example, it can represent the relationship between cost and production levels in business.

Topic

Linear Functions

Definition

Slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Description

Slope-intercept form is one of the most commonly used forms of linear equations. It provides a clear way to understand the slope and y-intercept of a line, making it easier to graph and interpret.

In real-world applications, slope-intercept form is used in various fields such as economics, physics, and engineering to model linear relationships. For example, it can represent the relationship between cost and production levels in business.

Topic

Linear Functions

Definition

The equation of a line from two coordinates can be determined by finding the slope between the two points and using it in the point-slope form of a linear equation.

Description

Finding the equation of a line from two coordinates is a fundamental skill in algebra. It involves calculating the slope between the two points and then using one of the points to form the equation in point-slope or slope-intercept form.

Topic

Linear Functions

Definition

The equation of a line from two coordinates can be determined by finding the slope between the two points and using it in the point-slope form of a linear equation.

Description

Finding the equation of a line from two coordinates is a fundamental skill in algebra. It involves calculating the slope between the two points and then using one of the points to form the equation in point-slope or slope-intercept form.

Topic

Linear Functions

Definition

The equation of a line from two coordinates can be determined by finding the slope between the two points and using it in the point-slope form of a linear equation.

Description

Finding the equation of a line from two coordinates is a fundamental skill in algebra. It involves calculating the slope between the two points and then using one of the points to form the equation in point-slope or slope-intercept form.

Topic

Linear Functions

Definition

The x-intercept is the point where a graph crosses the x-axis, indicating the value of x when 𝑦 y is zero.

Description

The x-intercept is a key concept in understanding the behavior of linear functions. It represents the point where the function's output is zero, providing insight into the function's roots and behavior.

In real-world applications, the x-intercept can be used to determine break-even points in business, where revenue equals costs, or to find the time at which a process starts or stops.

Topic

Linear Functions

Definition

The x-intercept is the point where a graph crosses the x-axis, indicating the value of x when 𝑦 y is zero.

Description

The x-intercept is a key concept in understanding the behavior of linear functions. It represents the point where the function's output is zero, providing insight into the function's roots and behavior.

In real-world applications, the x-intercept can be used to determine break-even points in business, where revenue equals costs, or to find the time at which a process starts or stops.

Topic

Linear Functions

Definition

The x-intercept is the point where a graph crosses the x-axis, indicating the value of x when 𝑦 y is zero.

Description

The x-intercept is a key concept in understanding the behavior of linear functions. It represents the point where the function's output is zero, providing insight into the function's roots and behavior.

In real-world applications, the x-intercept can be used to determine break-even points in business, where revenue equals costs, or to find the time at which a process starts or stops.

Topic

Linear Functions

Definition

The y-intercept is the point where a graph crosses the y-axis, indicating the value of y when x is zero.

Description

The y-intercept is a fundamental concept in understanding the behavior of linear functions. It represents the initial value of the function when the input is zero, providing insight into the function's starting point.

In real-world applications, the y-intercept can be used to determine initial conditions in various scenarios, such as the starting balance in a bank account or the initial position of an object in motion.

Topic

Linear Functions

Definition

The y-intercept is the point where a graph crosses the y-axis, indicating the value of y when x is zero.

Description

The y-intercept is a fundamental concept in understanding the behavior of linear functions. It represents the initial value of the function when the input is zero, providing insight into the function's starting point.

In real-world applications, the y-intercept can be used to determine initial conditions in various scenarios, such as the starting balance in a bank account or the initial position of an object in motion.

Topic

Linear Functions

Definition

The y-intercept is the point where a graph crosses the y-axis, indicating the value of y when x is zero.

Description

The y-intercept is a fundamental concept in understanding the behavior of linear functions. It represents the initial value of the function when the input is zero, providing insight into the function's starting point.

In real-world applications, the y-intercept can be used to determine initial conditions in various scenarios, such as the starting balance in a bank account or the initial position of an object in motion.

Topic

Statistics and Probability

Definition

A scatterplot is a graphical representation of the relationship between two numerical variables.

Description

Scatterplots are essential tools in statistics for visualizing the correlation between two variables. They are widely used in fields like economics and biology to identify trends and relationships in data.

For students, understanding scatterplots is important for interpreting data visually and analyzing the strength and direction of relationships between variables. This skill is crucial for developing their ability to conduct statistical analyses and draw meaningful conclusions from data.

In this interactive, review seven commonly used data displays. Provides a quck review tool for a unit on data analysis. Note: the download is the Teacher's Guide.

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In this Slide Show, learn how graph data in a scatterplot using the graph window. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

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Related Resources

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

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