Constant of Proportionality In Words
Constant of Proportionality Equations
Tables and Graphs
Unit Rates/Proportions
Similar Figures and Scale Factor
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
Navelle earns $12 per hour. Write an equation that represents Navelle's earnings.
y = 12x
100
What is the constant of proportionality?
The constant of proportionality is $1.50 per ticket.
100
Every 2.5 hours, a machine produces
2250 basketballs. What is the unit rate in basketballs per hour?
900 basketballs per hour
100
These triangles are similar. What is the value of x?
x = 7.5 units
200
Lenasia earned $640 in a 40-hour work week.
What is Lenasia's rate of pay per hour?
Lenasia earns $16 per hour.
200
Gianna reads 27 pages in 9 minutes. At What rate does Gianna read?
Write an equation for this relationship.
Gianna reads 3 pages per minute.
y = 3x
200
Does this table represent a proportional relationship? Explain.
No, the ratio of y/x is not constant so there is no COP.
200
Cody mows 1/4 of a yard in 3/4 of an hour. How long will it take him to mow the entire yard?
3 hours
200
What scale factor was used to go from the original image to the scaled drawing? Write your answer as a simplified fraction.
scale factor = 3/5
300
A helicopter propeller spins 2400 revolutions in 4 minutes. What is the constant of proportionality (k), in revolutions per minute?
k = 600 RPM.
300
Maxine works at law office. The equation y = 135x represents her earnings.
If Louis works at the same law office and earns $6000 in 50 hours, are his earnings per hour proportional to Maxine's? Explain
No, Maxine's earns $135 per hour and Louis earns $120 per hour, so their rate of pay is not the same. No COP.
300
A graph represents a proportional relationship if what two things are true about the graph?
1. It is a straight line
2. It passes through the origin
300
Ash walks 1 1/2 miles in 9/10 of an hour. What is their speed in miles per hour? Give your answer as a simplified mixed number.
1 2/3 miles per hour
300
What is the AREA of the second rectangle if the scale factor enlarging the first rectangle was 1.5?
12 x 4.5 = 54 square cm
400
Jeff earned $400 working a 40-hour work week.
a) Write an equation if x is number of hours and y is dollars earned.
b) How much does Jeff make if he works for 45.5 hours?
a) y = 10x
b) $455
400
The equation y = 65x represents the rate of speed on a highway, in miles per hour. Let x represent the number of hours driven and y represent the total miles driven.
a) How long was Francis driving if he drove 292.5 miles at the speed limit?
b) How far did James travel if he drove for 3 hours at the speed limit?
a) 4.5 hours
b) 195 miles
400
a) What is the constant of proportionality of this graph? Simplify as a fraction.
b) What type of slope does this graph have?
k = 1/6
positive slope
400
The relationship between your weight on the Earth and your weight on the moon is proportional. If you weigh 90 pounds on Earth, you would weigh 15 pounds on the moon. How much would weigh on the moon if you weighed 120 pounds on Earth?
20 pounds on the moon.
400
The scale of a room in a blueprint is 2 inches : 3 feet. A window in the same blueprint is 5 inches wide.
What is the width of the actual window in feet?
7.5 feet wide
500
Janine sells 16 apples for $8.00.
a) Write an equation if x is the number of apples and y is the total cost?
b) How many apples would she sell for $26?
a) y = 0.5x
b) 52 apples
500
If Jackson ate hamburgers at a rate of 3.5 hamburgers per minute and Jacen ate hamburgers at a rate of 4.7 hamburgers per minute, write an equation that could represent how many more hamburgers Jacen can eat more than Jackson.
y = 1.2x
500
Which has the smaller constant of proportionality? Explain.
The graph?
or the word problem: Jesse completed 10 laps in 18 minutes. How many laps did he run in 1 minute?
The graph problem. The COP in the word problem is 5/9 of a lap per minute and the COP in the graph is 2/3 of a lap per minute.
2/3 < 5/9
500
Diego makes bracelets. It takes him 4 2/3 hours to complete 2 bracelets. How much of a bracelet can he make in one hour?
3/7 of a bracelet in one hour.
500
What is the AREA of the scaled triangle if the given scaled factor is used to reduce the triangle shown below.
6.75 square feet