Using Graphs to Relate
Two Quantities
Objective:
To represent mathematical
relationships using graphs
*
• Think about a real world example where
something is dependent on time?
• Can you think of another real world example of
two things being dependent of each other (w/o
using time)
Problem #1: Analyzing a Graph
a) The graph shows the volume
of air in a balloon as you blow it
up, until it pops.
•
What are the variables?
• Describe how the variables are related at
various points on the graph.
Problem #1: Analyzing a Graph
b) The graph shows the length
of a board as time increases.
• What are the variables in
the graph?
• Describe how the variables
are related at various points
on the graph.
Problem #1
Got It?
The graph shows the cost of a
cell phone as the number of
minutes of calls increases.
• What are the variables in
the graph?
• Describe how the variables
are related at various points
on the graph.
Problem #2: Matching a Table & a Graph
a) A band allowed fans to download its new video
from its Web site. The table shows the total
number of downloads after 1, 2, 3, and 4 days.
Which graph could represent the data shown in in
the table?
Problem #2: Matching a Table & a Graph
b) The table shows the amount of sunscreen left in
a can based on the number of times the sunscreen
has been used. Which graph could represent the
data shown in the table?
Problem #2
Got It?
The table shows the total number of customers at a
car wash after 1, 2, 3, and 4 days of its grand
opening. Which graph could represent the data
shown in the table?
Problem #3: Sketching a Graph
a) A model rocket rises quickly and then slows to as
stop as its fuel burns out. It begins to fall quickly
until the parachute opens, after which it falls slowly
back to Earth. What sketch of a graph could
represent the height of the rocket during its flight?
Label each section.
Problem #3: Sketching a Graph
b) Suppose you start to swing yourself on a
playground swing. You move back and forth and
swing higher in the air. Then you slowly swing to a
stop. What sketch of a graph could represent how
your height from the ground might change over
time? Label each section.
If you jumped
from the swing
instead of slowly
swinging to a
stop, how would
the graph be
different?
Problem #3
Got It?
When Matt jogs on the treadmill, he gradually
increases his speed until he reaches a certain level.
Then he jogs at this level for several minutes. Then
he slows to a stop and stretches. After this he
increases to a speed that is slightly higher than
before and jogs at this speed for a short while before
slowing to a stop again. What is a possible sketch of
a graph that shows Matt’s jogging speed during his
workout? Label each section.
*Homework
Textbook Page 237 – 238; #1 – 13 All