CONSTANT OF PROPORTIONALITY!

WHAT IS IT? •A constant ratio in any proportional relationship•Really just another name for unit rate!

Remember, to be constant means it never changes!

WITH RATIO TABLES

Miles 50 100 150 200

Gallons

2 4 6 8

502 =

?1Find the

unit rate!

÷2

÷225 miles per gallon

This means our constant of proportionality is 25, so if we divide the miles by gallons we should always get 25.Let’s check!

𝟏𝟎𝟎÷𝟒=𝟐𝟓𝟏𝟓𝟎÷𝟔=𝟐𝟓𝟐𝟎𝟎÷𝟖=𝟐𝟓

Find the constant of proportionality between the gallons and the miles.

TRY THIS ONE!

Number of Apples

9 27 36

Cost $3.00 $9.00 $12.00

Find the constant of proportionality between the gallons and the miles.

Find the

unit rate!

93=

?1

÷3

÷3Constant of proportionality = 3

Let’s Check!𝟐𝟕÷𝟗=𝟑𝟑𝟔÷𝟏𝟐=𝟑

WITH GRAPHS

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5020406080

100120140160180200

Hours

Mile

s

(0,0)(1,45)

(2,90)

(3,135)(4,180

)

451

902

1353 4

yx

180

Y 45 90 135 180X 1 2 3 4

Find the constant of proportionality.

To find our constant of proportionality we have to

divide!

45

1= 45 90

2= 45

135

3= 45 180

4= 45

So, our constant of proportionality is 45.

Y 45 90 135 180X 1 2 3 4

Do you see that our x value multiplied by our constant of proportionality is our y value? We could write this like: y=45(x)

IMPORTANT!We will ALWAYS be able to write our constant of

proportionality as an equation that looks like

this: y=kx.

Just like in our last example! y=45x.

And k will always be our constant of proportionality!

WHAT CAN WE DO WITH IT?

• Population Density: Finding the constant of proportionality by dividing the population by the area.• Finding how many per 1 square mile

POPULATION DENSITYWildlife conservationists are concerned that the deer population might not be constant across the National Forest. The scientists found that there were 144 deer in a 16 square mile area of the forest. In another part of the forest, conservationists counted 117 in a 13 square mile area. Then a third conservationist counted 216 deer in a 24 square mile area of the forest. Do the conservationists need to be worried? Deer Square miles Do we have a

constant of proportionality?

144 16117 13216 24

14416¿9

1171321624

¿9

¿9

YES!

POPULATION DENSITYSo do the conservationists need to be worried?

NOPE! The deer population is constant in the National Forest.Let’s write an equation!

If we multiply our square miles by 9 we will have the number of deer. So our equation will look like:

Deer Square miles Constant of proportionality

144 16 9117 13 9216 24 9Deer = 9 x Miles

ORy=9x