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 .