Unit 5, Lesson 10
Equations of All Kinds of Lines
Accelerated 7
Preparation
Lesson Narrative
In this lesson, students extend previous work writing equations of lines to include equations for horizontal and vertical lines. Horizontal lines can still be written in the form but because in this case, the equation simplifies to . Students interpret this to mean that, for a horizontal line, the value does not change, but can take any value. This structure is identical for vertical lines except that now the equation has the form and it is the value that does not change while can take any value.
Note that while the equation of a vertical line cannot be written in the form , it can be written in the form , with . In this lesson, students encounter a context where this form arises naturally: A rectangle with length , width , and perimeter of 50 can be described by the equation .
This lesson is optional. Students will see additional work in future lessons with equations of the form . Consider using this lesson if students would benefit from seeing additional contexts that cannot easily be expressed using .
- Create multiple representations of a 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 $x=a$.
Let’s write equations for vertical and horizontal lines.
Required Preparation
Take a piece of string 50 centimeters long and tie the ends together to be used as demonstration in the third activity.
Cut a piece of string 50 cm long.