Section B Section B Checkpoint

Problem 1

A new park is planted with grass seed. Line ℓ\ell shows the height of the grass every week:

  1. A field nearby already has grass that is currently 3 inches tall. This grass grows 4 inches taller every week. Graph the height of this grass on the same set of axes as the grass just planted in the new park and label it line kk.
  2. Write an equation that represents the grass growing in the field where ww is the number of weeks and hh is the height of the grass in inches.
  3. Which set of grass is growing faster? Explain how you know.
Show Solution
Solution
  1. See graph

  2. h=4w+3h=4w+3 (or equivalent)
  3. Both sets of grass are growing at the same rate. Sample reasoning: The slope of line ℓ\ell is 4, which means it is growing 4 inches every week. This is the same for the grass in the nearby field. The lines are parallel, so they have the same slope. This also means they have the same rate of change.
Show Sample Response
Sample Response
  1. See graph

  2. h=4w+3h=4w+3 (or equivalent)
  3. Both sets of grass are growing at the same rate. Sample reasoning: The slope of line ℓ\ell is 4, which means it is growing 4 inches every week. This is the same for the grass in the nearby field. The lines are parallel, so they have the same slope. This also means they have the same rate of change.