You are planning an ornamental garden that has a total area of 200 square feet.
There are two sizes of ornamental plants you have chosen for your garden. Each small plant requires
2.5 square feet of space and each large plant requires 8 square feet of space. This situation can be
modeled by the equation
where
is the number of small plants
and
is the number of large plants to be placed in the
garden.
Part A: Find the intercepts of the graph of the equation.
Part
B: Graph the equation.
Part C: What do the intercepts mean in this
situation?
Part D: What are three possible numbers of small plants and large plants
that you can plant in the garden?
Part E: What is the slope of this
line?
Part F: Write the equation in slope-intercept form.
Part G:
You decide to enlarge the space for the garden to a total of 240 square feet which means the new
model will be
. Graph this equation on the same coordinate plane
you used in
Part B.
Part H: As you compare the two graphs, did
increasing the size of the garden change the slope or
-intercept? Describe any changes
that occurred.