Question

The quantities x and y are proportional. x y 15 5 25 8, start fraction, 1, divided by, 3, end fraction 33 11 Find the constant of proportionality left parenthesis, r, the right parenthesis in the equation y, equals, r, x.

Answer 1

Question:

The quantities x and y are proportional.

x 15 25

y 5 8⅓

Find the constant of proportionality.

Answer:

r = ⅓

Step-by-step explanation:

To find the constant of proportionality, we make use of the following formula

y = rx

Where y is the given data in the y row

r is the constant of proportionality

x is the given data in the x row.

Using the first values of x and y.

When x = 15, y = 5.

So,

y = rx becomes

5 = r * 15

5 = 15r

Divide through by 15

5/15 = 15r/15

⅓ = r

r = ⅓

Taking the second values of x and y

when x = 25, y = 8⅓

So,

y = rx becomes

8⅓ = r * 25

8⅓ = 25r

Convert mixed fraction to improper fraction

25/3 = 25r

Divide through by 25

25/3 ÷ 25 = 25r/25

25/3 * 1/25 = r

25/75 = r

⅓ = r

r = ⅓

Notice that r = ⅓ is the same for both values of x and y.

Hence, the constant of proportionality is ⅓

Answer 2

Answer:

The value of the constant of proportionality is

r = 1/3

Step-by-step explanation:

Given the quantities:

x: 15 ---- 25

y: 5 ------ 8⅓

We are required to find the constant of proportionality in the equation: y = rx

For x = 15, y = 5.

Using these in

y = rx

we have

5 = r × 15

5 = 15r

Divide both sides by 15

r = 5/15 = 1/3

For x = 25, y = 8⅓

Using these in

y = rx

we have

8⅓ = r × 25

8⅓ = 25r

25/3 = 25r (because 8⅓ = 25/3)

Divide both sides by 25

r = (25/3)/25

r = 1/3

We have a constant r to be 1/3, this is the value for the constant of proportionality.