Question

is the relationship between the values in the table to the right a direct variation, an inverse variation, or neither? if the relationship is a direct or inverse variation, then write an equation to model the variation.

is the relationship between the values in the table a direct variation, an inverse variation, or neither?

inverse
neither
direct

table:

x	y
8	20
16	30
22	40

Explanation:

Step1: Recall Direct and Inverse Variation

Direct variation: \( y = kx \) (constant ratio \( \frac{y}{x} \)). Inverse variation: \( xy = k \) (constant product).

Step2: Check Direct Variation (Ratio \( \frac{y}{x} \))

For \( x = 4, y = 10 \): \( \frac{10}{4} = 2.5 \)
For \( x = 8, y = 20 \): \( \frac{20}{8} = 2.5 \)
For \( x = 16, y = 30 \): \( \frac{30}{16} = 1.875 \) (not 2.5)
Ratio not constant, so not direct.

Step3: Check Inverse Variation (Product \( xy \))

For \( x = 4, y = 10 \): \( 4 \times 10 = 40 \)
For \( x = 8, y = 20 \): \( 8 \times 20 = 160 \) (not 40)
Product not constant, so not inverse.

Answer:

Neither