This lesson introduces the idea that any line in the plane can be considered a vertical translation of a line through the origin. The notion of a negative -intercept is also introduced.

Students begin by identifying lines that could be images of a given line under a translation, observing that they will be parallel to the original line. Next students graph two situations on the same coordinate plane that involve the same rate of change but with different initial values, observing how the graph of one line can be described as a translation of the other.

Then students identify equations that all represent the same line. In previous lessons, the terms in the expression were more likely to be arranged as because the situation involved a starting amount and then added on a multiple. In this lesson, is more likely because the situation involves starting with a proportional relationship and shifting it up or down.

Finally, students match cards that have lines presented as equations, graphs, descriptions, and tables (MP2, MP7).