Illustrative Math Alignment: Grade 8 Unit 3

Linear Relationships

Lesson 9: Slopes Don't Have to be Positive

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 2	Math Example--Linear Function Concepts--The Point-Slope Formula: Example 2 Topic The Point-Slope Form Description In this example, we explore finding the equation of a line with a slope of -1 passing through the point (5, 2). Applying the point-slope formula y - y1 = m(x - x1), we substitute the given values to obtain y - 2 = -(x - 5). After simplification, the final equation of the line is y = -x + 7.	Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 3	Math Example--Linear Function Concepts--The Point-Slope Formula: Example 3 Topic The Point-Slope Form Description This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of 3 passing through the point (-2, 7). Using the formula y - y1 = m(x - x1), we substitute the given values to get y - 7 = 3(x - (-2)). After simplification, the resulting equation is y = 3x + 13.	Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 4	Math Example--Linear Function Concepts--The Point-Slope Formula: Example 4 Topic The Point-Slope Form Description In this example, we explore finding the equation of a line with a slope of -5 that passes through the point (-7, 5). Applying the point-slope formula y - y1 = m(x - x1), we substitute the given values to obtain y - 5 = -5(x - (-7)). After simplification, the final equation of the line is y = -5x - 30.	Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 5	Math Example--Linear Function Concepts--The Point-Slope Formula: Example 5 Topic The Point-Slope Form Description This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of 2 passing through the point (-2, -3). Using the formula y - y1 = m(x - x1), we substitute the given values to get y - (-3) = 2(x - (-2)). After simplification, the resulting equation is y = 2x + 1.	Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 6	Math Example--Linear Function Concepts--The Point-Slope Formula: Example 6 Topic The Point-Slope Form Description This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of -7 passing through the point (-8, -5). Using the formula y - y1 = m(x - x1), we substitute the given values to get y - (-5) = -7(x - (-8)). After simplification, the resulting equation is y = -7x - 61.	Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 7	Math Example--Linear Function Concepts--The Point-Slope Formula: Example 7 Topic The Point-Slope Form Description In this example, we explore finding the equation of a line with a slope of 4 passing through the point (8, -2). Applying the point-slope formula y - y1 = m(x - x1), we substitute the given values to obtain y - (-2) = 4(x - 8). After simplification, the final equation of the line is y = 4x - 34.	Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 8	Math Example--Linear Function Concepts--The Point-Slope Formula: Example 8 Topic The Point-Slope Form Description This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of -2 passing through the point (3, -8). Using the formula y - y1 = m(x - x1), we substitute the given values to get y - (-8) = -2(x - 3). After simplification, the resulting equation is y = -2x - 2.	Point-Slope Form
Math Example: The Slope As Rise Over Run: Three Examples	In this set of math examples, see how slope is calculated for a staircase based on measures for the rise and the run.	Slope
MATH EXAMPLES--Teacher's Guide: Equations of Parallel and Perpendicular Lines	MATH EXAMPLES--Teacher's Guide: Equations of Parallel and Perpendicular Lines This Teacher's Guide provides an overview of the 32 worked-out examples that show how to find the equation of a line parallel or perpendicular to a given line and through a given point. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Applications of Linear Functions and Graphs of Linear Functions
MATH EXAMPLES--Teacher's Guide: Equations of Parallel and Perpendicular Lines	MATH EXAMPLES--Teacher's Guide: Equations of Parallel and Perpendicular Lines This Teacher's Guide provides an overview of the 32 worked-out examples that show how to find the equation of a line parallel or perpendicular to a given line and through a given point. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Applications of Linear Functions and Graphs of Linear Functions
MATH EXAMPLES--Teacher's Guide: Finding the Equation of a Line, Given Two Points	MATH EXAMPLES--Teacher's Guide: Finding the Equation of a Line, Given Two Points This Teacher's Guide provides an overview of the 12 worked-out examples that show how to find the equation of a line, given two points. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Applications of Linear Functions and Graphs of Linear Functions
MATH EXAMPLES--Teacher's Guide: Graphs of Linear Functions in Slope-Intercept Form	MATH EXAMPLES--Teacher's Guide: Graphs of Linear Functions in Slope-Intercept Form This Teacher's Guide provides an overview of the 13 worked-out examples that show how to graph a linear function, given the slope and y-intercept. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Applications of Linear Functions and Graphs of Linear Functions
MATH EXAMPLES--Teacher's Guide: The Midpoint Formula	MATH EXAMPLES--Teacher's Guide: The Midpoint Formula This Teacher's Guide provides an overview of the 20 worked-out examples that show how to use the Midpont Formula. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Midpoint Formula
MATH EXAMPLES--Teacher's Guide: The Point Slope Form	MATH EXAMPLES--Teacher's Guide: The Point Slope Form This Teacher's Guide provides an overview of the 8 worked-out examples that show how to find the equation of a lineusing the Point Slope Form. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Applications of Linear Functions and Graphs of Linear Functions
MATH EXAMPLES--Teacher's Guide: The Slope Formula	MATH EXAMPLES--Teacher's Guide: The Slope Formula This Teacher's Guide provides an overview of the 21 worked-out examples that show how to use the Slope Formula. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Applications of Linear Functions and Slope
MATH EXAMPLES--The Slope Formula	MATH EXAMPLES--The Slope Formula The complete set of 21 examples that make up this set of tutorials. NOTE: The download is a PPT file.	Applications of Linear Functions and Slope
Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Easy)	Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Easy) This is part of a collection of math quizzes on the topic of finding the Equation of a Line Given Two Points. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Point-Slope Form and Slope-Intercept Form
Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Hard)	Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Hard) This is part of a collection of math quizzes on the topic of finding the Equation of a Line Given Two Points. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Point-Slope Form and Slope-Intercept Form
Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Medium)	Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Medium) This is part of a collection of math quizzes on the topic of finding the Equation of a Line Given Two Points. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Point-Slope Form and Slope-Intercept Form
Paper-and-Pencil Quiz: Linear Equations Given m and b (Easy)	Paper-and-Pencil Quiz: Linear Equations Given m and b (Easy) This is part of a collection of math quizzes on the topic of Linear Equations. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Slope-Intercept Form
Paper-and-Pencil Quiz: Linear Equations Given m and b (Hard)	Paper-and-Pencil Quiz: Linear Equations Given m and b (Hard) This is part of a collection of math quizzes on the topic of Linear Equations. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Slope-Intercept Form
Paper-and-Pencil Quiz: Linear Equations Given m and b (Medium)	Paper-and-Pencil Quiz: Linear Equations Given m and b (Medium) This is part of a collection of math quizzes on the topic of Linear Equations. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Slope-Intercept Form
Paper-and-Pencil Quiz: Slope Formula (Easy)	Paper-and-Pencil Quiz: Slope Formula (Easy) This is part of a collection of math quizzes on the topic of the Slope Formula. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Slope
Paper-and-Pencil Quiz: Slope Formula (Hard)	Paper-and-Pencil Quiz: Slope Formula (Hard) This is part of a collection of math quizzes on the topic of the Slope Formula. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Slope
Paper-and-Pencil Quiz: Slope Formula (Medium)	Paper-and-Pencil Quiz: Slope Formula (Medium) This is part of a collection of math quizzes on the topic of the Slope Formula. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Slope
Promethean Flipchart: Algebra Jeopardy	In this Promethean Flipchart, review key concepts from linear functions using a Jeopardy-style game. Note: The download for this resources is the Promethean Flipchart.	Applications of Equations and Inequalities
Quizlet Flash Cards: Slope Formula, Set 01	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 01	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 02	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 02	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 03	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 03	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 04	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 04	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 05	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 05	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 06	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 06	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 07	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 07	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 08	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 08	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 09	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 09	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 10	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Quizlet Flash Cards: Slope Formula, Set 10	Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6	Slope
Video Transcript: Algebra Applications: Linear Functions	Video Transcript: Algebra Applications: Linear Functions Linear Expressions, Equations, and Functions Linear Expressions	Applications of Linear Functions and Graphs of Linear Functions
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Video Transcript: Application of Ratios: Roofs and Ramps	Video Transcript: Application of Ratios: Roofs and Ramps What Are Ratios? A ratio is the relationship between two or more quantities among a group of items.	Applications of Ratios, Proportions, and Percents
Video Transcript: Application of Ratios: Roofs and Ramps	Video Transcript: Application of Ratios: Roofs and Ramps What Are Ratios? A ratio is the relationship between two or more quantities among a group of items.	Applications of Ratios, Proportions, and Percents