A unit rate can also be called a constant of proportionality. The constant of proportionality describes the rate at which variables is an equation change.
To find constant of proportionality, we may use the formula
k = y/x
k = 6/2 ==> 3
Check if we have the same constant of proportionality for all the values.
k = 9/3 ==> 3
k = 15/5 ==> 3
k = 18/6 ==> 3
Determine the constant of proportionality for each table. Express your answer as y = kx.
Problem 1 :
Every concrete block weighs _____ kilograms.
Solution :
Weight 3 blocks = 30 kg
Weight of 1 block = 30/3
= 10 kg
Equation of constant of proportionality :
y = 10x
So, weight of 1 block is 10 kg.
Every concrete block weighs 10 kilograms.
Problem 2 :
For every can of paint you could paint ___ bird houses.
Solution :
Using 5 cans of paint, we are able to paint 15 bird houses.
1 can of paint used to paint = 15/5
= 3 houses.
Equation of constant of proportionality :
y = 3x
For every can of paint you could paint 3 bird houses.
Problem 3 :
For every vote of Faye there were ____ votes of Victor.
Solution :
If Faye gets 9 votes, then Victor will get 342 votes
If number of votes is 1 for Faye, then 342/9 = 38 votes for Victor.
Equation of constant of proportionality :
y = 38x
For every vote of Faye there were 38 votes of Victor.
Problem 4 :
Every single chocolate bars has ____ calories
Solution :
In 6 chocolate bars, there are 1212 calories
In 1 chocolate bar, we have 1212/6 = 202 calories
Equation of constant of proportionality :
y = 202x
So,
Every single chocolate bars has 202 calories.
Problem 5 :
For each piece of chicken it costs _____ dollars.
Solution :
Price of 7 pieces of chicken = $14
Price of 1 piece of chicken = 14/7
= $2
Equation of constant of proportionality :
y = 2x
So,
For each piece of chicken it costs 2 dollars.
Problem 6 :
For every box of candy ___ is the price.
Solution :
Cost of 2 boxes of candy = 32
Cost of 1 box of candy = 32/2
= 16
Equation of constant of proportionality :
y = 16x
For every box of candy 16 is the price.
Find the constant of proportionality, then use it to fill the missing values in the table
Problem 7 :
Solution :
Constant of proportionality k = y/x
= 36/9
k = 4
The proportional relationship will be the form of y = kx
y = 4x
x = y/4
When y = 16, x = 16/4 ==> 4
When x = 5, y = 4(5) ==> 20
When y = 8, x = 8/4 ==> 2
Problem 8 :
Solution :
Constant of proportionality k = y/x
= 2/6
k = 1/3
The proportional relationship will be the form of y = kx
y = (1/3)x
x = 3y
When y = 4, x = 3(4) ==> 12
When x = 15, y = (1/3)(15) ==> 5
When x = 9, y = (1/3)(9) ==> 3
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