Lesson plan

# Lesson 11: Equations of All Kinds of Lines

teaches Common Core State Standards 8.EE.B http://www.corestandards.org/the-standards
teaches Common Core State Standards MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards 8.EE.B.6 http://corestandards.org/Math/Content/8/EE/B/6

# Lesson 11: Equations of All Kinds of Lines

In previous lessons, students have studied lines with positive and negative slope and have learned to write equations for them, usually in the form $$y=mx+b$$. In this lesson, students extend their previous work to include equations for horizontal and vertical lines. Horizontal lines can still be written in the form $$y=mx+b$$ but because $$m$$=0 in this case, the equation simplifies to $$y=b$$. Students interpret this to mean that, for a horizontal line, the $$y$$ value does not change, but $$x$$ can take any value. This structure is identical for vertical lines except that now the equation has the form $$x=a$$ and it is $$x$$ that is determined while $$y$$ can take any value.

Note that the equation of a vertical line cannot be written in the form $$y=mx+b$$. It can, however, be written in the form $$Ax+By=C$$ (with $$B$$ = 0). This type of linear equation will be studied in greater detail in upcoming lessons. In this lesson, students encounter a context where this form arises naturally: if a rectangle has length $$ℓ$$ and width $$w$$ and its perimeter is 50, this means that $$2ℓ+2w=50$$.

Lesson overview

• 11.1 Warm-up: Which One Doesn’t Belong: Pairs of Lines (5 minutes)
• 11.2 Activity: All the Same (15 minutes)
• Includes "Are you Ready for More?" extension problem
• There is a digital applet in this activity.
• 11.3 Activity: Same Perimeter (15 minutes)
• There is a digital applet in this activity.
• Lesson Synthesis
• 11.4 Cool-down: Line Design (5 minutes)

Learning goals:

• Comprehend that for the graph of a vertical or horizontal line, one variable does not vary, while the other can take any value.
• Create multiple representations of linear relationship, including a graph, equation, and table.
• Generalize (in writing) that a set of points of the form $$(x,b)$$ satisfy the equation $$y=b$$ and that a set of points of the form $$(a,y)$$ satisfy the equation $$x=a$$.

Learning goals (student facing):

• Let’s write equations for vertical and horizontal lines.

Learning targets (student facing):

• I can write equations of lines that have a positive or a negative slope.
• I can write equations of vertical and horizontal lines.

Required materials

• String

Required preparation:

• Take a piece of string 50 centimeters long and tie the ends together to be used as demonstration in the third activity.

Glossary:

• Access the complete Grade 8 glossary.

Standards

• This lesson builds on the standard: CCSS.7.G.AMO.7.GM.A

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.