Constant Proportionality from Tables
Constant of Proportionality from Graphs
Constant of Proportionality from Words
Constant of Proportionality and Equations
COP requirements
100
Drew paints portraits. Find the constant of proportionality if it is a proportional relationship
Time (in hours) = x Number of portraits = y
1 5
2 10
3 15
4 20
5 portraits per hour
100
Find the constant of proportionality with correct units
k =46 miles per hour
100
Sophia bought 12 desserts for a total cost of $33.60.
Use the unit rate to write an equation relating the cost in dollars c to the number of desserts d.
c = 2.80d
100
Find the constant of proportionality: y = 7x
k = 7
100
Ellen ran the first 182 miles of a race in 13 hours. What was her average rate, in miles per hour, for this first 182 miles of the race?
14mph
200
The table shows the amount earned by Harry for selling ice cream. Find k.
Cups Sold = x 3 5 7 9
Earnings ($) = y 12 20 28 36
CoP = 4
200
What is K with proper units?
k = 1.2 miles per hour
200
State whether each scenario is proportional or not proportional.
A golf cart rental store charge $50 as a flat fee, plus $25 per hour
A car travels 60 miles in 1 hour, 120 miles in 2 hours, and 180 miles in 3 hours
A student earns $12 for each hour of tutoring
Not proportional
Proportional
Proportional
200
An airplane travels 900 miles in 4 hours. The equation y = 225x models this situation.
What is the constant of proportionality? _______________
k = 225
200
Marcus and his family are planning a vacation that involves horseback riding. Horseshoe Ranch charges a $15.50 ranch entrance fee plus $10.50 per hour to rent horses. What would the cost be for 3 and 4 hours?
$47.00, $57.50
300
Fred wrote notes during an exam. Find the CoP if it is a proportional relationship.
Notes (pages) 8 9 10 11
Time (in hours) 18 19 20 21
It is not proportional, there is no CoP.
300
Find the constant of proportionality with correct units
5 gallons per min
300
To make juice, Michael combines 1/4 liters of water and 2/3 scoops of juice mix. What is the CoP (scoops per liter)?
8/3 or 2 2/3 scoops per liter
300
The total cost of renting a frozen yogurt machine for 4 hours is $72. What equation can be used to model the total cost y for renting the frozen yogurt machine for x hours?
y = 18x
300
State whether the situation forms a proportional relationship or non proportional relationship.
A. The equation is in y = kx form.
B. In a table, the ratios are equivalent.
C. In a graph, the line passes through the origin and it is a straight line.
a. Proportional
b. Proportional
c.Proportional
400
A ferry transports bikes to an island. Write k
Number of bikes (x) 10 12 14
Number of trips (y) 5 6 7
k = 0.5
400
Find k with proper units.
k = 3 gallons per minute
400
For every rose planted, Josh plants 5 daisies. If he wants to plant a total of 48 roses and daisies, how many roses should he plant?
8
400
The number of milk bottles sold can be determined by the equation P = 0.35n, where P is the number of bottles of milk and n is the number of boxes opened. Find the constant of proportionality with correct units.
k = 0.35 bottles per box
400
what are the two qualifications to tell if a line on a graph is proportional?
it passes through the origin and it is a straight line
500
Alice bought comics. Find k if the table shows a proportional relationship.
Number of comics 2 4 6
Price (dollars) 6 12 18
k = 3 dollars per comic
500
Find the constant of proportionality.
60
500
A dog can walk 1 1/2 miles in 3/4 of an hour. How far can the dog walk in an hour?
2 miles
500
On average, Anna can drive 31 miles on every gallon of gasoline. If she fills up her tank for $2.19 per gallon, how much will it cost her to drive 434 miles?
$30.66
500
A painter can paint 150 square feet per hour. He charges $0.33 per square foot. Today he paints for 6.5 hours. How much will he charge?
$321.75