Proportional Relationships in Tables
In each row, the values in the left column can be ______ by the constant to get the values in the right column.
Multiplied
When the x value is 1, the y value represents the ______.
Constant of Proportionality
The graph of proportional relationship is a _____ line through the _____.
1st Blank: straight
2nd Blank: origin
Jamesha swims at a constant speed. It takes her 0.5 minutes to swim 0.25 laps. Find her unit rate, in minutes per lap.
2 minutes
0.5 / 0.25 = 2 minutes ~ Constant
At a grocery store, 1 pound of mangoes costs $1.50. Find the cost for 3 pounds of mangoes at this rate.
$4.50
1.50 / 1 = $1.50 ~ Constant
3 * 1.50 = $4.50
Which table shows a proportional relationship with a constant of proportionality of 4?
A B C D
2 | 4 2 | 12 2 | 8 2 | 16
3 | 6 3 | 18 3 | 12 3 | 24
5 | 10 5 | 30 5 | 20 5 | 40
C
The equation y=5x represents the relationship between the number of packs (x) and the number of juice boxes (y). What is the meaning of the 5 in this situation.
There are 5 juice boxes per pack.
5 * 1 pack = 5 juice boxes
5 * 2 pack = 10 juice boxes
...
In Jessie's recipe for macaroni and cheese, the amount of cheese (y) is proportional to the amount of macaroni (x). Explain what the ordered pairs (4,3) means in this context.
3 ounces of cheese are used with 4 ounces of macaroni
OR 4 ounces of macaroni are used with 3 ounces of cheese
Which expression has the same value as the complex fraction below?
(1/4)
_____
(1/3)
1/4 * 3/1
Keep, Change, Flip
The number that both values in a ratio table can be multiplied by to get the values of an equivalent ratio is called the _______.
Scale Factor
In each row, the values in the right column can be ______ by the constant to get the values in the left column.
Divided
At track practice, Chelsea jogs several laps around the track at a constant speed. The equation d=4t describes the distance (d), in meters, Chelsea runs in (t) seconds. How far will Chelsea run in 10 seconds?
40 meters
d=4t
d=4 * (10)
d=40 meters
Samantha says that a graph shows a proportional relationship as long as a straight line can be drawn through the points. Is she correct?
No. A graph shows a proportional relationship when a straight line goes through the points AND it passes through the origin.
In a grocery store, 5 pounds of grapes are sold for $17. Find the unit price of grapes in dollars per pound.
$3.40 dollars
17 / 5 = $3.40 ~ Constant
Victor rode his bike 24 miles in 2 hours. On Victor's next ride, he will travel at the same rate for 0.5 hours. How far will he ride?
6 miles
24 / 2 = 12 miles ~ Constant
0.5 * 12 = 6 miles
What is the constant of proportionality in the table below?
2 | 8
4 | 16
7 | 28
4
8 / 2 = 4
16 / 4= 4
28 / 7= 4
All rows produce a value of 4, so 4 is the constant
The number of gallons of gasoline (g) that a car uses is proportional to the number of miles (d) that it travels. A constant of 25 is determined using a table showing the amount of gas a car needs to travel different distances. Write an equation to represent this relationship.
d = 25g
A new hotel charges $90 per night for a room. Suppose that the hotel owner creates a graph that shows the relationship between the number of nights (x) and the cost (y), in dollars. What does the point (0,0) mean in the context of this situation?
For 0 nights, the hotel charges $0
Henry bought 0.25 pounds of jelly beans for $2. What is the scale factor used to identify the cost for 2 pounds of jelly beans?
8 is the scale factor
2 / 0.25 = 8 ~ Scale Factor
2 * 8 = $16
Julio has a toy train that travels around a circular track at a constant rate. The train completes 2 laps every 1.5 minutes. At what rate is the train traveling, in minutes per lap?
0.75 minutes per lap
1.5 / 2 = 0.75 minutes ~ Constant
What is the constant of proportionality in the table below?
8 | 2
12 | 3
20 | 4
There is NO constant
2 / 8 = 0.25
3 / 12 = 0.25
4 / 20 = 0.2
The rows did not ALL produce the same value, so there is no constant
Eric makes papier-mache for an art project by mixing glue with water. The relationship between the amount of glue (g) and water (w) is proportional and represented by the equation g=3w. How much water is needed if Eric uses 24 cups of glue?
8 cups of water
g = 3w
24 = 3w
24/3 = 3w/w
8 = w
Kiara types at a constant rate where time = x and number of words = y. A graph shows the points (2, 80) and (3, 120). How many words can Kiara type in 1 minute?
40 words
80 / 2 = 40
120 / 3 = 40
1 * 40 = 40 words ~ Constant
A custodian uses 0.5 cups of liquid soap to clean 0.125 of the cafeteria floor. At this rate, how many cups of soap will they need to clean the entire cafeteria floor?
HINT: What number value represents the WHOLE cafeteria floor?
4 cups
0.5 / 0.125 = 4 cups ~ Constant
Jannelle's father is repainting the fence in their backyard. It took him 0.8 hour to paint 8 yards of fencing. Identify the scale factor used to calculate the number of yards of fencing her father can paint at 4 hours at this rate.
5 is the scale factor
4 / 0.8 = 5 ~ Scale Factor
8 * 5 = 40 yards