Constant of Proportionality
Direct Variation: Tables
Direct Variation: Missing Value
All things proportional
Challenge Lane‼️
100
What is K with proper units?
k = 1.2 miles per hour
100
The table shows the amount earned by Harry for selling ice cream. If y varies directly with x, find the missing y value in the table below.
Cups Sold = x 3 5 7 9
Earnings ($) = y 12 20 y 36
y = 28
100
If y varies directly as x, then when y = 9 then x = 3.
What is y when x = 12?
y = 36
100
Julie brought 5 pounds of cans to a recycling place and was paid $2. Find the unit rate. (cost per pound)
$0.40/pound
100
Which situation represents a proportional relationship between the number of laps run by each student and their time?
Desmond's Table
200
A ferry transports bikes to an island. What is k?
Number of bikes (x) 10 12 14
Number of trips (y) 5 6 7
k = 0.5
200
Logan works at a local taco shop and makes $9 per hour. If Logans pay is varies directly with the number of hours he works, complete the table to represent his situation. (Find the missing y values.)
**There are TWO answers.**
Time (x) 0 1/2 1 9
Pay (y) y y 9 81
When x = 0, y = 0
When x = 1/2, y= 4.5
200
y varies directly as x. Find the values as indicated:
If y = -18 when x = 9, find y when x = 7
y = -14
200
What is k mean in y=kx?
Constant of Proportionality
200
The graph shows the cost of purchasing T-shirts.
Find the constant rage of change for the graph.
The cost increases by $9 per shirt.
300
Find the constant of proportionality with correct units
k =46 miles per hour
300
Drew paints portraits. If the number of portraits varies directly with the number of hours spent on each painting, find the missing x value in the table.
Time (in hours) = x Number of portraits = y
x 5
2 10
3 15
4 20
x = 1
5 portraits per hour
300
In the following problem, y varies directly as x, if y = -3 when x = -4.
Find x when y = 12
x = 16
300
What is the fraction version of...
-2.6666666....
-2 ⅔
300
Determine if each equation represents a direct variation. Select yes or no.
a.
b.
c.
d.
A) No
B) Yes
C) Yes
D) No
400
Fred passed notes during class throughout the day. Find the constant of proportionality.
People (x) 8 9 10 11
Notes (y) 18 19 20 21
It is not proportional - there is no COP.
400
Alice bought old/used/cheap comics. Find the k (CoP with correct units) if the price in dollars varies directly with the number of comic books she purchased.
Number of comics (x) 6 12 -9
Price (dollars) (y) 2 4 -3
k = 1/3
400
y varies directly as x. Find the values as indicated:
If y = 6 when x = 9, find x when y = 12
x = 18
400
What are the two qualifications to tell if a line on a graph is proportional?
1. Straight Line
2. Passes through the origin
400
The height of two plants is recorded after 1, 2, and 3 weeks as shown in the graph at the right. Which plants’ growth represents a proportional relationship between time and height? Explain.
Plant B... BECAUSE it is a straight line and goes through the origin.
500
Find the constant of proportionality with correct units
60 miles per hour
500
Shawty earns $84 for a 7 hour shift at Chick-fil-la. The amount of money she earns, y, varies directly to the number of hours worked, x.
Show this proportional relationship by completing the table.
Time (in hours) = x Money Earned = y
0 _______
1/2 _______
5 _______
_______ 180
Time (in hours) = x Money Earned = y
0 ___0____
1/2 ___6____
5 ___60____
___15____ 180
500
On a graph, y varies directly with x, so that the following coordinate is used... (-12, 8).
Find the missing y coordinate in the following sequence.
(-18, y)
y = 12 OR (-18, 12)
500
What is a synonym for constant of proportionality?
Unit Rate or Direct Variation
500
DAILY DOUBLE!!!
Assume the situation is proportional. Write and solve by using a proportion.
Sheila mixed 3 ounces of blue paint with 2 ounces of yellow paint. She decided to create 20 ounces of the same mixture. How many ounces of yellow paint does Sheila need for the new mixture?
What is 8 ounces?