Sam walked to a nearby shop to purchase a gallon of ice cream. The shop is 400 meters from his house, and it took him 4 minutes to get there. At the shop, it took 2 minutes to choose a flavor and purchase the ice cream. He walked home in 3 minutes, at a faster pace than before so the ice cream wouldn’t melt.

Draw a graph that models Sam’s distance from home (in meters) in terms of time (in minutes). Label the graph with appropriate intervals and units.

The axes and units for the graph are given in the problem statement. The range of the graph is also given, but figuring the domain requires a little arithmetic. We assume the walking pace is constant, so the graph will be piecewise linear.

Axes

The vertical (y) axis is labeled with what the graph is modeling, "distance from home (in meters)." The horizontal (x) axis is labeled with what the model is in terms of "time (in minutes)."

The range of the graph is 0 to 400 meters, the range of distances Sam may be from home.

The domain of the graph is 0 to 9 minutes. The time it takes to complete the trip is 4 minutes to the shop, 2 minutes at the shop, and 3 minutes coming home, for a total of 4+2+3 = 9 minutes.

Graph

We are given that points on the graph will be (0, 0), (4, 400), (6, 400), and (9, 0). That is Sam is ...

at home at 0 minutes
400 meters from home (at the shop) after 4 minutes
remaining 400 meters from home for 2 more minutes (until 6 minutes)
at home after 3 more minutes (at 9 minutes).

Since we assume walking is at a steady pace, we connect these dots with straight lines. The resulting graph is attached.