Question

Determine if x and y are inversely proportional. If applicable, find the constant of variation.

Answer 1

x and y are inversely proportional , constant of proportion k = 30

When x and y are inversely proportional, their relationship is expressed by the equation y=​k/x , where k is the constant of proportionality.

Start with the inverse proportionality equation: y=k/x, where k is the constant of proportionality.

Multiply both sides of the equation by k=xy.

To verify that k is constant, use given ordered pairs from the table.

a. For the pair (0.1, 300):

k=0.1×300=30.

b. For the pair (0.5, 60):

k=0.5×60=30.

c. For the pair (75, 0.4):

k=75×0.4=30.

d. For the pair (100, 0.3):

k=100×0.3=30.

In each case, the product k remains constant at 30.

Therefore, it can be concluded that x and y are inversely proportional, and the constant of proportionality k is consistently 30.

Answer 2

x and y are inversely proportional , constant of proportion k = 30

Explanation:

If x and y are inversely proportional then the equation relating them is

y =
`(k)/(x)` ← k is the constant of proportion

multiply both sides by y , then

k = xy

to check that k is constant use the ordered pairs from the table

(0.1, 300 )

k = 0.1 × 300 = 30

(0.5, 60 )

k = 0.5 × 60 = 30

(75, 0.4 )

k = 75 × 0.4 = 30

(100, 0.3 )

k = 100 × 0.3 = 30

thus x and y are inversely proportional with constant of proportion k = 30