Question

suppose that x and y vary inversely and x = 1 when y = 9. write a function that models the inverse variation. graph the function and find y when x = 20.

write a function that models the inverse variation.

y = \square (simplify your answer.)

Explanation:

Step1: Recall inverse variation formula

The formula for inverse variation is \( y = \frac{k}{x} \), where \( k \) is the constant of variation.

Step2: Find the constant \( k \)

We know that \( x = 1 \) when \( y = 9 \). Substitute these values into the inverse variation formula:
\( 9=\frac{k}{1} \)
This simplifies to \( k = 9\times1 = 9 \).

Step3: Write the inverse variation function

Substitute \( k = 9 \) back into the inverse variation formula \( y=\frac{k}{x} \). So the function is \( y=\frac{9}{x} \).

Answer:

\( \frac{9}{x} \)