IM 8.3.8 Lesson: Translating to y=mx+b
The diagram shows several lines. You can only see part of the lines, but they actually continue forever in both directions.
Which lines are images of line under a translation?
For each line that is a translation of f, draw an arrow on the grid that shows the vertical translation distance.
Compare the second line with the first line. How much more money does Diego have after 1 hour of babysitting? 2 hours? 5 hours? hours?
Write an equation for each line.
Experiment with moving point A.
Place point in three different locations above the -axis. For each location, write the equation of the line and the coordinates of point .
Place point in three different locations below the -axis. For each location, write the equation of the line and the coordinates of point .
In the equations, what changes as you move the line? What stays the same?
Why do you think this is the case?
There are 4 pairs of lines, A–D, showing the graph, a, of a proportional relationship and the image, h, of a under a translation. Match each line h with an equation and either a table or description. For the line with no matching equation, write one.
If the line passes through the origin, what equation is displayed?
A student says that the graph of the equation is the same as the graph of , only translated upwards by 8 units. Do you agree? Why or why not?