Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation.

y = 2.5 when x = 9

1) k = 3.6; xy = 3.6

2) k = 22.5; y = 22.5x

3) k = 22.5; xy = 22.5

4) k = 3.6; y = 3.6

Answer: 3) k = 22.5; xy = 22.5

Step-by-step explanation:

If two variables are inversely proportional, it means that an increase in the value of one variable would cause a corresponding decrease in the other variable. Also, a decrease in the value of one variable would cause a corresponding increase in the other variable.

Given that y varies directly with x, if we introduce a constant of proportionality, k, the expression becomes

y = k/x

If y = 2.5 when x = 9, then

2.5 = k/9

k = 9 * 2.5 = 22.5

Therefore, an equation for the inverse variation is

y = 22.5/x

xy = 22.5