Graphing Proportional Relationships
Equations of Proportional Relationships
Identifying Proportional Relationships
Multi-step Ratio Problems
Fractional Unit Rates
100
What is the ordered pair for the origin?
** Don't forget your parentheses around the ordered pair! **
(0,0)
100
Is this equation proportional? y= 3x
If so, what is the constant of proportionality? (K)
Yes
k=3
100
Ms. Levy sells 10 Chick-fil-A sandwiches every hour. Is the relationship between sandwiches sold and time proportional? If so, what is the constant of proportionality?
Yes, k = 10
100
6 pounds of candy cost $22.44.
What is the unit price?
$3.74/pound
100
If 5/6 gallons of paint covers 1/4 of the house, then how much paint is needed for the entire house?
5/6 divide by 1/4
5/6*4/1= 10/3
10/3 gallons or 3 1/3 gallons
200
A relationship between two quantities that is changing at a CONSTANT rate is:
a. proportional
b. nonproportional
a. proportional
200
Is this equation proportional? If so what is the constant of proportionality? (K=)
y= 4x + 10
Not proportional
200
Is the graph a proportional relationship? Why?
NO
The line does not go through the origin.
200
You can drive 450 miles on 18 gallons of gas. How far can you travel on one gallon?
25 miles per gallon
200
A pool pump fills 1/6 of the pool in 1/3 hour. How much of the swimming pool is filled in one hour?
1/6 of pool divided by 1/3 hour
1/6*3/1=1/2
1/2 the pool
300
Recipe 1 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
300
Write an equation for the table given the table is proportional.
y = 3/2 x
or y = 1 1/2x
or y = 1.5x
300
What is the formula to find the constant of proportionality in a graph?
k=y/x
300
Which set of paper towels is the better buy? 9 rolls for $8.73 or 14 rolls for $12.32? Explain.
$12.32/14 rolls= $0.88/roll
$8.73/9 rolls= $0.97/roll
14 rolls is the better buy because it has the cheapest unit price.
300
A smoothie recipe calls for 2 1/4 cups of frozen mango. If the recipe serves two, how many cups of frozen mango is needed to serve one?
2 1/4 cups / 2 servings
9/4 cups / 2 servings
9/4*1/2=9/8
Answer: 1 1/8 or 9/8 cups
400
What are the two rules to know if a graph is proportional?
1. The line is straight (no curves or zig-zags)
2. The line goes through the origin (0,0)
400
Is this equation proportional? If so what is the constant of proportionality? (K=)
y= ¾ x
proportional
k= 3/4
400
Is the table proportional? Justify your answer.
No. The number of students to buses ratio is not constant. 24/1 does not equal 45/2.
400
Shannon ran 400 meters in 88 seconds. Carly ran 100 meters in 12 seconds. Determine the speed of each runner in meters per second. Round your answer to the nearest hundredths. Who is running faster?
Shannon:
400m / 88 sec. = 4.55 meters per sec.
Carly:
100m / 12 sec. = 8.33 meters per sec.
Carly is running faster. She is running more meters per second than Shannon.
400
Laundry detergent is priced 20 ounces for $3.40 or 14 ounces for $2.10. What is the unit rate of the laundry detergent that is the better value?
$3.40 / 20 ounces = $0.17 per ounce
$2.10 / 14 ounces = $0.15 per ounce
Answer: 14 for $2.10
500
Is this graph proportional? Explain WHY.
Yes, it is a straight line that goes through the origin.
500
Using this graph, What is the equation? Write your constant of proportionality as a FRACTION. 
y= 1/6x
500
Is the table proportional? Justify your answer.
Yes, it is proportional. The ratio of money to hours worked is constant, $9/hour.
500
A candy company can make 360 pounds of chocolate in 6 hours. How much can they make in 10 hours? Show your work.
360 pounds / 6hrs. = 60 pounds per hour
60*10= 600
Answer: 600 pounds
500
A recipe for sugar cookies requires 2 cups of flour for every 2/3 cups of sugar. At this rate, how many cups of sugar should be used if 5 cups of flour are included?
2/3 cup of sugar / 2 cups of flour
2/3*1/2=1/3
1/3 cup of sugar per cup of flour
1/3*5=5/3
Answer: 1 2/3 c of flour or 5/3 cups of flour