Question

Does the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.
x : 2 4 8 12
y : 10 5 5/2 5/3

A) direct variation ; y = 20/x
B) inverse variation ; xy = 20
C) direction variation ; y = 20x
D) inverse variation ; y/x = 20

Answer 1

Answer:

Option B is correct

Inverse variation , xy = 20

Step-by-step explanation:

Inverse variation states:

If $y \propto \frac{1}{x}$

then the equation is in the form of:

$y = \frac{k}{x}$

or

xy = k            ....[1]

As per the statement:

Given the data:

x : 2 4 8 12

y : 10 5 5/2 5/3

Let any value of x and y to find k:

x = 4 and y = 5

Substitute in [1] we have;

$4 \cdot 5 = k$

⇒20 = k

or

k = 20

then we get;

xy = 20

Check:

$xy = 20$

Substitute x = 12  and y = 5/3

$12 \cdot \frac{5}{3} = 20$

⇒$20 = 20$ true.

Therefore, the the data in the table represent a inverse variation and an equation to model the data in the table is, xy = 20

Answer 2

B) xy=20

Inverse because it is of the form y=k/x, intuitively you can see that as x increases y decreases, hence "inverse variation".