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
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 3	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 3 Topic Linear Functions Description This example demonstrates how to find the equation of a horizontal line passing through the points (2, 3) and (7, 3). The slope is calculated as 0 since both y-coordinates are the same. Using the point-slope form, y - y1 = m(x - x1), the equation becomes y - 3 = 0(x - any x-value), which simplifies to y = 3, representing a horizontal line.	Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 4	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 4 Topic Linear Functions Description This example illustrates how to find the equation of a vertical line passing through the points (5, 3) and (5, 8). The slope is undefined because both x-coordinates are the same, resulting in division by zero when using the slope formula. This indicates a vertical line, and the equation is simply x = 5.	Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 5	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 5 Topic Linear Functions Description This example demonstrates how to find the equation of a line passing through the points (-6, 1) and (-2, 3). The slope is calculated using the formula (y2 - y1) / (x2 - x1), resulting in a slope of 1/2. Using the point-slope form of a line, y - y1 = m(x - x1), the equation is derived and simplified to y = (1/2)x + 4.	Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 6	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 6 Topic Linear Functions Description This image shows a graph with two points (-8, 4) and (-4, 2). The slope is calculated as (y2 - y1) / (x2 - x1), resulting in a slope of -1/2. The equation of the line is derived using point-slope form and simplified to y = -(1/2)x. The slope is calculated as -1/2, and the line equation is determined using point-slope form: y = -(1/2)x.	Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 7	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 7 Topic Linear Functions Description This image shows a graph with two points (-7, 5) and (-1, 5). The slope is calculated as zero since the y-values are equal. The equation of the line is horizontal, simplified to y = 5. The slope is 0, indicating a horizontal line. The equation is y = 5.	Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 8	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 8 Topic Linear Functions Description This image shows a graph with two points (-5, 6) and (-5, 3). The slope is undefined because the x-values are equal. This results in a vertical line at x = -5. The slope is undefined, indicating a vertical line at x = -5.	Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 9	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 9 Topic Linear Functions Description The image shows a coordinate plane with two points (-5, -4) and (-4, -1) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated, and the equation is derived using point-slope form. The slope is calculated as (y2 - y1) / (x2 - x1) = (-1 - (-4)) / (-4 - (-5)) = 3 / 1 = 3. Using point-slope form, y - y1 = m(x - x1), the equation is derived as y + 1 = 3(x + 4), which simplifies to y = 3x + 11.	Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 1	Math Example--Linear Function Concepts--The Point-Slope Formula: Example 1 Topic The Point-Slope Form Description This example demonstrates how to find the equation of a line using the point-slope form. The given information includes a slope of 5 and a point (6, 5) through which the line passes. Using the point-slope formula y - y1 = m(x - x1), we can substitute the known values to derive the equation y - 5 = 5(x - 6). Simplifying this equation leads to the final result: y = 5x - 25.	Point-Slope Form
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: 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 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 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 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 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

Illustrative Math Alignment: Grade 8 Unit 3

Linear Relationships

Lesson 11: Equations of All Kinds of Lines

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