Constant of Proportionality In Words
Constant of Proportionality Equations
Tables and Graphs
Unit Rates
Comparing Proportional Relationships
100
Haneef sends 45 emails in 15 minutes.
How many emails did he send per minute?
He sent 3 emails per minute.
100
Moris earns $12 per hour. Write an equation that represents his earnings.
y = 12x
100
Is this table proportional? Explain.
The table is proportional because if we divide each cost by the number of tickets, we see the constant of proportionality is $1.50 per ticket.
100
Every 2.5 hours, a machine produces
2250 basketballs. What is the unit rate of this proportional relationship?
In other words, how many basketballs are produced per hour?
900 basketballs per hour
100
Which graph has the greatest constant of proportionality?
Line a
200
Nala earned $640 in a 40-hour work week.
What is her hourly rate of pay?
Nala earns $16 per hour.
200
Ava reads 27 pages in 9 minutes. At What rate does Ava read?
Write an equation for this relationship.
She reads 3 pages per minute.
y = 3x
200
Is this table proportional? Explain.
The table is not proportional because when we divide the sales of ice cream by each temperature, we do not get the same answer.
200
What is the general equation of a proportional relationship?
y = kx
200
Which relationship has the greater constant of proportionality? Explain.
y = 7x
or
?
The equation y = 7x has a greater constant of proportionality because:
7>6
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
Jessie works at law office. The equation y = 135x represents her earnings. Determine how much money she makes if she works 40 hours.
Jessie earns $5,400 in 40 hours.
300
A graph represents a proportional relationship if:
1.
2.
1. It is a straight line
2. It passes through the origin
300
Dewa babysat her little brother for 4 hours and made $60. What is her unit rate?
$15.00 per hour
300
Which has the greater constant of proportionality? Explain.
The equation y = 1.5x or the table below:
The equation has the greater constant of proportionality because 1.5 is greater than 1.25.
400
Hector earned $400 working a 40-hour work week.
Find his hourly wage and use it to predict how much he will make if he works for 47 hours.
Hector makes $10 per hour and would make $470 in 47 hours.
400
The equation y = 55x represents the rate of a highway speed limit, in miles per hour. Let x represent the number of hours driven and y represent the total miles driven.
How long was Jake driving if he drove 247.5 miles at the speed limit.
Hake drove for 4.5 hours.
400
What is the constant of proportionality in this graph?
The constant of proportionality is 1/6.
400
Jhorlin mowed 5 lawns and made $100. How much money did he make per lawn?
He made $20 per lawn.
400
Which has the smaller constant of proportionality? Explain.
The graph:
The word problem:
Keon completed 10 laps in 18 minutes. How many laps did he run in 1 minute?
The graph is 2/3 of a lap per minute, or 6/9 of a lap per minute.
The word problem is 5/9 of a lap per minute.
Since 6/9 > 5/9, then 2/3 is greater than 5/9 so the word problem gives the smaller constant of proportionality.
500
Jaiden 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.
Jaiden would earn $32 for selling 64 apples.
500
If Caden ate hamburgers at a rate of 4.7 hamburgers per minute and Josh ate hamburgers at a rate of 3.5 hamburgers per minute, write an equation that could represent how many more hamburgers Caden can eat more than Josh.
y = 1.2x
500
What is the constant of proportionality in this graph?
The constant of proportionality is 5.
500
Isiah earned 104 points in a trivia game. He correctly answered 26 questions in the game. How many points was each question worth?
4 points per question
500
Which relationship has the greater constant of proportionality? The table or the graph? How do you know?
Well A has the greater constant of proportionality.
Well A pumps water at a faster rate at 2.75 barrels per hour. Barrel B pumps water at 2.5 barrels per hour.