Question

Fill in the missing values in the table. Then determine the constant of proportionality.

Answer 1

Answer:

Blank 1) 2 1/3 yards : 7 Feet

Blank 2) 1 yards : 3 Feet

Blank 3) 2 yards : 6 Feet

Blank 4) 1.5 yards : 4.5 Feet

Therefore, the constant of proportionality is: k = 3

Step-by-step explanation:

We know that when 'y' varies directly with 'x', we get the equation

y ∝ x

y = kx

Here, k is the constant of proportionality.

From the table, taking the first two points to determine the constant of proportionality.

Yards                Feet

1/2                       1.5

1/3                        1

Using the equation

substituting y = 1.5 and x = 1/2

y = kx

k = y/x

k = (1.5) / (1/2)

k = 1.5 / 0.5

k = 3

also substituting  y = 1 and x = 1/3

k = y/x

k = 1 / (1/3)

k = 3

As the constant of proportionality is the same.

• Therefore, the constant of proportionality = k = 3

Determining Blank 1

Yards = x = 2 1/3 = 7/3

y = blank 1 = Feet ?

k = 3

Using the equation

y = kx

blank 1 = Feet = y = 3 (7/3)

blank 1 = Feet = y = 7

• Therefore, Blank 1 = y = Feet =  7

In other words,

When Yards = 2 1/3, then Feet = 7

Determining Blank 2

Feet = y = 3

Blank 2 = x = yards ?

k = 3

Using the equation

y = kx

Blank 2 = x = yards =  y/k    

Blank 2  = x = yards = 3/3

Blank 2 = x = yards = 1

• Therefore, Blank 2 = yards = x = 1

In other words,

When Yards = 1, then Feet = 3

Determining Blank 3

yards = x = 2

Blank 3 = y = Feet ?

k = 3

Using the equation

y = kx

y = Blank 3 = Feet = 3(2)

y = Blank 3 = Feet = 6

• Therefore, Blank 3 = Feet = y = 6

In other words,

When Yards = 2, then Feet = 6

Determining Blank 4

Feet = y = 4.5

Blank 4 = x = Yards ?

k = 3

Using the equation

y = kx

x = Blank 4 = y/k

x = Blank 4 = 4.5/3

x = Blank 4 = 1.5

• Therefore, Blank 4 = x = Yards= 1.5

In other words,

When Yards = 1.5, then Feet = 4.5

Summary:

Blank 1) 2 1/3 yards : 7 Feet

Blank 2) 1 yards : 3 Feet

Blank 3) 2 yards : 6 Feet

Blank 4) 1.5 yards : 4.5 Feet

Therefore, the constant of proportionality is: k = 3