The variable \( y \) is indirectly proportional to the variable \( x \). If \( x=3 \) and \( y=2 \), calculate the value of \( y \) if \( x=18 \).

When two variables are **indirectly proportional** (also known as **inversely proportional**), it means that as one variable increases, the other decreases in such a way that their product remains constant. Mathematically, this relationship can be expressed as: \[ y = \frac{k}{x} \] where: - \( y \) is the dependent variable, - \( x \) is the independent variable, and - \( k \) is the constant of proportionality. ### Step 1: Find the Constant of Proportionality (\( k \)) Given: - \( x = 3 \) - \( y = 2 \) Plug these values into the equation to solve for \( k \): \[ 2 = \frac{k}{3} \] Multiply both sides by 3: \[ k = 2 \times 3 = 6 \] So, the equation relating \( y \) and \( x \) is: \[ y = \frac{6}{x} \] ### Step 2: Calculate \( y \) When \( x = 18 \) Now, substitute \( x = 18 \) into the equation: \[ y = \frac{6}{18} \] Simplify the fraction: \[ y = \frac{1}{3} \] ### **Answer:** When \( x = 18 \), the value of \( y \) is \( \frac{1}{3} \).