6th Grade Math Textbook, Fundamentals

Distance from Home

Time

Graph A

Distance from Home

Time

Graph B

Distance from Home

Time

Graph C

368 Chapter 13

13-9

Graph a Situation

Objective To choose a representation for a

situation• To sketch a graph for a situation

• To interpret a graph or a specific part of a graph in
  terms of the situation it represents

Rafael leaves home and drives to the airport. He takes an
airplane to Mexico City, stays for 1 week, and then flies
home again. Rafael drives back home from the airport.

Which graph best represents this situation?

Sometimes a graph does not show a function, but a situation. In the graphs above,

a line slanting up or down represents a varying rate of change. The steeper the

slant, the faster the rate of change. The less steep the slant, the slower the rate

of change. A horizontal line represents a constant (zero) rate of change.

To see if a graph and a situation match, break the situation into a sequence

of events. Then see if each event fits the graph and if the events are shown in

the correct order.

Event 1:Rafael drives from home to the airport.

Event 2:Rafael takes a plane to Mexico City.

Event 3:Rafael stays in Mexico City for 1 week.

Event 4:Rafael flies home.

Event 5:Rafael drives home from the airport.

Graph A

The story begins and ends

at home. Therefore, the

graph should begin at (0, 0)

and end on the x-axis. This

graph cannot describe the

situation.

Graph B

While this graph shows a

departure and a return

home, it does not show

Rafael staying in one place

(Mexico City) for a period

of time. So this graph does

not describe the situation.

Graph C

This graph begins and ends at

home. As Rafael’s distance from

home increases, the line on the

graph steepens. The horizontal

line represents the time Rafael

spent in Mexico City. Then as

Rafael’s distance from home

decreases, the steepness of the

line lessens.

Graph C matches the situation.

So Graph C best represents the situation.