Transcript Constant of Proportionality and Equations of Graphs

Constant of Proportionality and
Equations of Graphs
Vocabulary
• Constant: a unique number that stays the same.
• Variable: placeholder for an unknown number.
• proportional relationship: is described by ordered
pairs that satisfy the equation y = kx where k is a
positive constant.
(y = kx)
example: y = 2x (1,2);(2,4);(3,6);(4,8)
• K: is the constant of proportionality which is the
unit rate.
• The unit rate and constant of proportionality
are the same. They both represent the same
number that is the value of the ration of y to x
• Brandon came home from school and
informed his mother that he volunteered to
make cookies for his entire grade level. He
needs 3 cookies for each of the 96 students in
7th grade. Unfortunately, he needed them for
the very next day! Brandon and his mother
determined that they can fit 36 cookies on
two cookie sheets.
• Is the number of cookies proportional to the
number of sheets used in baking?
# of cookie sheets
# of cookies baked
Unit Rate
2
36
18
4
10
16
• The constant of proportionality is _____
• What is the meaning of the constant of
proportionality?
• It took 2 hours to bake 8 sheets of cookies. If
Brandon and his mother start baking at
4:00pm, what time will they finish?
8:00 pm
• Suzette and Margo want to prepare crepes for all of the
students in their French class. A recipe makes 20
crepes with a certain amount of flour, milk, and 2 eggs.
The girls know that they already have plenty of flour
and milk but need to determine the number of eggs
needed to make 50 crepes because they are not sure
they have enough eggs for the recipe.
• Considering the amount of eggs necessary to make the
crepes what is the constant of proportionality?
• What does the constant of proportionality mean in the
context of this problem?
• How many eggs will be needed to make 50 crepes?
Interpreting Graphs of
Proportional Relationships
Record the coordinates and what do they
mean in the context of the situation?
If Grandma only has 1 cup of sugar left,
how many dozen cookies can she
make?
How many dozen cookies can she make
with 0 cups of sugar?
What is the unit rate, what is the constant of proportionality, and what does it mean?
If you started at 0 and moved one unit horizontally, how many units would you have to go
Vertically to hit the line?
Why are we always moving at the same rate vertically?
Must every graph have a point (1,r)?
Can you tell if this is a
proportional relationship by
looking at the graph?
How long can a person shower
with 15 gallons of water?
With 60?
What are the coordinates of
pointA and what do they mean?
Can you use the graph to find the
unit rate?
What is the unit rate?
Write an equation to represent the relationship of number of gallons used
and length of a shower
Abort the Mission!
• What two points are always on the graph of a
proportional relationship?
• How can you use the unit rate to create a
table, graph, or equation?
• How can you determine the unit rate from a
table, graph, or equation?
Exit Ticket
• Great Rapids White Watering Company rents rafts for
$125 per hour.
• Explain why the point (0,0) and (1, 125) are on the
graph and what they mean.
• Write and equation that can be used to find the rental
cost for any number of hours
• How much does it cost to rent a raft for 6.5 hours?