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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

Respuesta :

irspow
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".

Answer:

Option B is correct

Inverse variation , xy = 20

Step-by-step explanation:

Inverse variation states:

If [tex]y \propto \frac{1}{x}[/tex]

then the equation is in the form of:

[tex]y = \frac{k}{x}[/tex]

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;

[tex]4 \cdot 5 = k[/tex]

⇒20 = k

or

k = 20

then we get;

xy = 20

Check:

[tex]xy = 20[/tex]

Substitute x = 12  and y = 5/3

[tex]12 \cdot \frac{5}{3} = 20[/tex]

⇒[tex]20 = 20[/tex] 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

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