Constant of Proportionality (Unit Rate)
Tables and Graphs
Proportional or Non-Proportional Relationships?
Scaled Copies
6th Grade Review
100
Jude sends 45 E-mails in 15 minutes.
How many E-mails did he send per minute?
He sent 3 E-mails per minute.
100
Proportional or Non-Proportional? If proportional, what is the CoP?
Proportional.
The relationship is constant because if we divide each cost per number of tickets, we see the constant of proportionality is $1.50 per ticket.
100
Proportional or Non-Proportional? Why?
Proportional.
Passes through origin
Straight line
100
When scaling a shape, what happens to the angles?
They do not change
100
Which temperature is warmer?
–5°C or –10°C
–5°C
200
Lenasia earned $640 in a 40-hour work week.
What is Lenasia's hourly rate of pay?
Lenasia earns $16 per hour.
200
Proportional or Non-Proportional? Explain.
This is not proportional because when we divide the sales of ice cream by each temperature, we do not get a constant rate.
200
Proportional or Non-Proportional? Why?
Proportional.
Passes through origin
Straight Line
200
When a scaled copy gets larger, the scale factor is _________
Greater than 1
200
DOUBLE JEOPARDY
Sydney’s fitness app says she has completed 70% of her goal for the week. Her goal is 50 miles. How far has she biked?
35 miles
300
A helicopter propeller spins 2400 revolutions in 4 minutes. What is the constant of proportionality (k), in revolutions per minute?
The constant of proportionality is k = 600 RPM.
300
A graph represents a proportional relationship if:
1.
2.
1. It is a straight line
2. It passes through the origin
300
Proportional or Non-Proportional? Why? Hint: set up ratio for each row and divide.
Proportional. Constant rate = $1.25
or $1.25 per 1lb. of bananas
300
What is the length of "?" if the two figures are scaled copies?
? = 20
300
Kai also wrote the equation y = 4x. One point that Kai wrote was (3, 12).
Use the equation to identify 3 other points on the graph.
(1,4), (2,8), (4,16), (5,20), (6,24), etc.
400
Jeff earned $400 working a 40-hour work week.
Find Jeff's hourly wage (earnings).
Jeff makes $10 per hour.
400
Proportional or Non-Proportional? How do you know?
Proportional.
1- Straight Line
2- Passes through the origin (0,0)
400
Proportional or Non-Proportional? Why?
Non-Proportional.
It is not a straight line.
400
What is the scale factor?
The scale factor is 0.5 or 1/2
400
Here's a recipe for two-ingredient pancakes:
Two-Ingredient Pancakes
Serves 4 People
● 6 eggs
● 2 bananas
How many eggs and how many bananas do you need to serve 6 people?
9 eggs and 3 bananas
500
Janine sells 16 apples for $8.00. What is the unit price for each apple?
How much would she earn if she sold 64 apples?
The unit price is $0.50 per apple.
Janine would earn $32.00 for selling 64 apples.
0.50/1=x/64
500
Does this table represent a proportional relationship between the cost and number of tickets?
No. It is non-proportional. The ratios are not the same.
Ex.
24/2=12
28/4 = 7
500
Proportional or Non-Proportional? Why?
Non-Proportional.
Does not pass through the origin.
500
If the scale factor is greater than 1, then the scaled copy will be smaller in comparison to the original figure.
False!
A scale factor greater than 1 will make the copy bigger than the original.
500
Which expression is equivalent to 20 − 8𝑑?
A. 2(4𝑑 − 10)
B. 4(5 − 8𝑑)
C. 4(5 − 2𝑑)
D. (20 − 8)𝑑
C. 4(5 − 2𝑑)
600
What is the COP in this equation?
y = 2/3x
2/3
600
What is the constant of proportionality?
1/3
600
If there is a graph of a straight line but it doesn't go through the point (0,0) is it proportional?
No.
600
If the original rectangle is 10ft by 8ft, what will the new area be if scaled by 2?
320 sq ft
600
Complete the number sentence with the symbol <, >, or =.
–5 ____–4. 5
–5 < –4. 5