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.

example: y = 2x (1,2);(2,4);(3,6);(4,8)

• K: is the constant of proportionality which is the unit rate.

(y = kx)

• 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?

• The constant of proportionality is _____• What is the meaning of the constant of

proportionality?

# of cookie sheets # of cookies baked Unit Rate

2 36 18

4

10

16

• 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 makewith 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 goVertically 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 showerwith 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?