Graphing Proportional Relationships
Identifying Proportional Relationships
Interpreting Points
Equations of Proportional Relationships
Equations of Proportional Relationships
100
What is the ordered pair for the origin?
** Don't forget your parentheses around the ordered pair! **
(0,0)
100
How do you find the constant of proportionality?
DIVIDE Y/X
100
Mrs. Martsching is selling shirts for a fundraiser.
She is plotting points on a graph to show her students how much she makes, in $money$.
What would the point (0,0) mean in this situation?
If she sells 0 shirts, she will make $0.
100
Is this equation proportional? y= 3x
If so, what is the constant of proportionality? (K)
Yes
k=3
100
When Trayvon goes to the batting cages, he uses 2 tokens for every 10 pitches.
There is a proportional relationship between the number of tokens Trayvon uses, x, and the number of pitches, y.
Write the equation.
y=5x
200
A relationship between two quantities that is changing at a CONSTANT rate is:
a. proportional
b. nonproportional
c. it depends on the relationship
a. proportional
200
Is the graph a proportional relationship? Why?
NO
Does not go through the origin
200
Mrs. Martsching is selling shirts for a fundraiser.
She plots points on a graph to show her students how much she makes, in $.
What would the point (1,8) mean in this situation?
Each shirt costs $8.
200
Is this equation proportional? If so what is the constant of proportionality? (K=)
y= 4x + 10
Not proportional
200
Dominic buys 10 boxes of raisins for $5.
There is a proportional relationship between the number of boxes of raisins he buys and the total cost.
Write the equation.
Reminder: this is in $.
y=0.50x
300
What are the two criteria for knowing if a graph is proportional?
1. The line is straight (to show a constant rate) - (LINEAR)
2. The line goes through the origin (0,0)
300
Is the table proportional? What is the COP?
No, it doesn't have one!
300
Mrs. Martsching is selling shirts for a fundraiser.
She plots points on a graph to show her students how much she makes, in $.
What would the point (18,144) mean in this situation?
It means that when Mrs. Martsching sells 18 shirts, she will make $144.
300
Is this equation proportional? If so what is the constant of proportionality? (K=)
y= ¾ x
proportional
k= 3/4
300
Does the equation y=12x match the following scenario?
Lia earns $39 for 3 hours of babysitting.
There is a proportional relationship between the number of hours Lia babysits, x, and the total amount of money she earns, y.
If yes, what is the cost per hour? If not write a new equation.
No. The cost per hour is $13. The new equation is y=13x.
400
Is this graph proportional? Explain WHY.
Yes, it is a straight line that goes through the origin.
400
Is the table proportional? What is the COP?
Yes, it is proportional. COP = 9
400
Mrs. Martsching is selling shirts for a fundraiser.
She plots points on a graph to show her students how much she makes, in $.
The equation for this situation is y=8x.
Would the point (8, 62) be on this graph? If not, why?
No. The point would be (8, 64).
400
Using this graph, What is the equation?
Write your constant of proportionality as a FRACTION. 
y= 1/6x
400
A gear makes 50 revolutions each minute.
It can be represented by the equation r=50t,
where r is the total revolutions and t is the number of minutes.
Bennett says that after 82 minutes, there will have been 4,100 revolutions.
Betty says that after 193 minutes there will have been 9,600 revolutions.
Who is correct?
Bennett is correct.
Betty should have 9,650 revolutions after 193 minutes.
500
A recipe for lemonade is given by the equation
y = 4x where x represents the cups of lemonade mix and y represents the cups of water.
If Tyler had 16 cups of lemonade mix, how many cups of water would he need for each recipe?
64 cups of water
500
How do you know if a table of data is proportional?
When you divide the y value by its x value, you get the same constant of proportionality (COP) in each row.
500
Mrs. Martsching is selling shirts for a fundraiser.
She plots points on a graph to show her students how much she makes, in $.
The equation for this situation is y=8x.
Would the point (73, 584) be on this graph? If not, why?
Yes. When Mrs. Martsching sells 73 shirts, she will make $584.
500
Write an equation for the table given the table is proportional.
y = 3/2 x
or y = 1 1/2x
or y = 1.5x
500
A wedding reception seats eight people at each table.
The relationship is represented by the equation p=8t, where p is the number of people and t is the number of tables.
Geoff says that for 104 people there should be 12 tables needed.
Ginger says that for 128 people you would need 16 tables.
Who is correct?
Ginger is correct.
Geoff would need 13 tables to accommodate 104 people.