Illustrative Math Alignment: Grade 8 Unit 3

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

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This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

Lesson Summary

In this lesson, students will explore different methods for graphing linear functions, strengthening their understanding of how algebraic equations relate to their graphical representations. The lesson covers:

By the end of this lesson, students will be proficient in graphing linear functions and interpreting their meaning in real-world applications.

This comprehensive lesson plan delves into the concept of slope as a measure of the rate of change in linear functions. Students will engage with various representations—graphs, tables, and real-world scenarios—to calculate and interpret slope effectively. The lesson emphasizes contextual understanding, enabling learners to connect mathematical concepts to everyday situations.

Key components of the lesson include:

Lesson Plan: Graphing Linear Equations

This is the second lesson in a five-part series on linear equations. It introduces students to graphing linear equations using slope-intercept form: $y = mx + b$. Students will learn to identify slope and y-intercept, plot points, and interpret graphs in real-world contexts. The lesson aligns with Common Core Standards 8.EE.B.5 and 8.EE.B.6.

In this lesson, students explore the properties of parallel and perpendicular lines in coordinate geometry. They will learn how to identify these lines based on their slopes, determine equations for parallel and perpendicular lines, and apply these concepts to solve real-world and mathematical problems.

Key concepts covered in this lesson include:

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Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = 2x + 4. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, 4), (1, 6), (2, 8), (3, 10), and (4, 12), illustrating how the y-value increases by 2 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = -x + 6. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, 6), (1, 5), (2, 4), (3, 3), and (4, 2), illustrating how the y-value decreases by 1 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = -x - 8. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, -8), (1, -9), (2, -10), (3, -11), and (4, -12), showing how the y-value decreases by 1 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates the creation of a table of x-y coordinates and the graphing of the linear function y = -x. The image displays both a graph and a table representing this function. The table includes coordinate pairs (0, 0), (1, -1), (2, -2), (3, -3), and (4, -4), illustrating how the y-value decreases by 1 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = 0.5x + 4. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 4), (1, 4.5), (2, 5), (3, 5.5), and (4, 6), showing how the y-value increases by 0.5 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = 0.1x - 5. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, -5), (1, -4.9), (2, -4.8), (3, -4.7), and (4, -4.6), illustrating how the y-value increases by 0.1 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = 0.2x. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 0), (1, 0.2), (2, 0.4), (3, 0.6), and (4, 0.8), showing how the y-value increases by 0.2 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = -0.5x + 7. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, 7), (1, 6.5), (2, 6), (3, 5.5), and (4, 5), illustrating how the y-value decreases by 0.5 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = -0.1x - 4. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, -4), (1, -4.1), (2, -4.2), (3, -4.3), and (4, -4.4), showing how the y-value decreases by 0.1 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = -0.6x. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, 0), (1, -0.6), (2, -1.2), (3, -1.8), and (4, -2.4), illustrating how the y-value decreases by 0.6 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = 0x. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 0), (1, 0), (2, 0), (3, 0), and (4, 0), showing how the y-value remains constant at 0 for all values of x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = 3x - 2. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, -2), (1, 1), (2, 4), (3, 7), and (4, 10), showing how the y-value increases by 3 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = 0x - 6. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, -6), (1, -6), (2, -6), (3, -6), and (4, -6), illustrating how the y-value remains constant at -6 for all values of x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = 0 * x + 4. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 4), (1, 4), (2, 4), (3, 4), and (4, 4), showing how the y-value remains constant at 4 for all values of x.

Topic

Linear Functions

Description

This example demonstrates the creation of a table of x-y coordinates and the graphing of the linear function y = 5x. The image displays both a graph and a table representing this function. The table includes coordinate pairs (0, 0), (1, 5), (2, 10), (3, 15), and (4, 20), illustrating how the y-value increases by 5 for each unit increase in x.

Topic

Linear Functions

Description

This example showcases the process of creating a table of x-y coordinates and graphing the linear function y = -2x + 5. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 5), (1, 3), (2, 1), (3, -1), and (4, -3), demonstrating how the y-value decreases by 2 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the creation of a table of x-y coordinates and the graphing of the linear function y = -3x - 4. The image displays both a graph and a table representing this function. The table includes coordinate pairs (0, -4), (1, -7), (2, -10), (3, -13), and (4, -16), showing how the y-value decreases by 3 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = -6x. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, 0), (1, -6), (2, -12), (3, -18), and (4, -24), illustrating how the y-value decreases by 6 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = x + 7. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 7), (1, 8), (2, 9), (3, 10), and (4, 11), showing how the y-value increases by 1 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates the creation of a table of x-y coordinates and the graphing of the linear function y = x - 8. The image displays both a graph and a table representing this function. The table includes coordinate pairs (0, -8), (1, -7), (2, -6), (3, -5), and (4, -4), illustrating how the y-value increases by 1 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = x. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 0), (1, 1), (2, 2), (3, 3), and (4, 4), showing how the y-value increases by 1 for each unit increase in x.

Topic

Rational Functions

Description

This example demonstrates the graph of the rational function y = 1 / x. The graph is a hyperbola with vertical and horizontal asymptotes, with the vertical asymptote occurring at x = 0. Students are tasked with graphing the function and determining its vertical asymptote.