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 mc020-2.jpg








inverse variation; xy = 20


direct variation; y =


direct variation; y = 20x


inverse variation; = 20

Answer 1

To determine whether the data represents a direct variation or an inverse variation, we need to analyze the relationship between \( x \) and \( y \) values in the table.

The given values are:
- For \( x = 2 \), \( y = 10 \)
- For \( x = 4 \), \( y = 5 \)
- For \( x = 8 \), \( y = ? \)
- For \( x = 12 \), \( y = ? \)

Now, to check if it represents an inverse variation, we look to see if the product \( xy \) is constant.

Calculating \( xy \) for the known pairs:
1. For \( x = 2; y = 10 \):
\( xy = 2 \times 10 = 20 \)

2. For \( x = 4; y = 5 \):
\( xy = 4 \times 5 = 20 \)

Since both products yield 20, it suggests there is an inverse variation because the product of \( x \) and \( y \) remains constant.

To find the general form of the equation for inverse variation, we use the formula:
\[
xy = k
\]
where \( k \) is the constant.

From our calculations, \( k = 20 \). Thus, the equation representing the inverse variation is:
\[
xy = 20
\]

Finally, since the original question provides multiple options, the correct choice is:
**inverse variation; xy = 20.**