Translations

This lesson develops a third way to understand an equation of a line in a coordinate plane. In previous lessons, students wrote an equation of a line by generalizing from repeated calculations using their understanding of similar triangles and slope. They also wrote an equation of a linear relationship by reasoning about initial values and rates of change, and they graphed the equation as a line in a coordinate plane. This lesson introduces the idea that any line in a plane can be considered a vertical translation of a line through the origin.

By Desmos Classroom

Learning goals: Learning Goals • Derive `y=mx+b` by graphing `y=mx` and the same graph shifted up using the translation that takes `\left(0,\ 0\right)` to `\left(0,\ b\right)`. • Connect the equations `y=b+mx` and `y=mx+b` to the graph. • Encounter a graph where the `y`-intercept is a negative value.