Question

1. suppose that y varies inversely with x. write a function that models the inverse function.

x = 7 when y = 3

\\( y = 21x \\)

\\( y = \frac{21}{x} \\)

\\( y = \frac{3}{7x} \\)

\\( y = \frac{3x}{7} \\)

Explanation:

Step1: Recall inverse variation formula

Inverse variation is modeled as \( y = \frac{k}{x} \), where \( k \) is the constant of variation.

Step2: Calculate k using given values

Substitute \( x = 7 \) and \( y = 3 \) into the formula: \( 3 = \frac{k}{7} \). Solve for \( k \): \( k = 3 \times 7 = 21 \).

Step3: Write the final function

Substitute \( k = 21 \) back into the inverse variation formula: \( y = \frac{21}{x} \).

Answer:

y = 21/x