Question

for the inverse variation equation (xy = k), what is the constant of variation, (k), when (x = -3) and (y = -2)?

-6

-\frac{2}{3}

\frac{3}{2}

6

Explanation:

🆕 New Concept Discovered: Inverse Variation
Two variables change in opposite directions

Step 1: Identify the given equation and values

The inverse variation equation is:

$$ xy = k $$

We are given the following values:

• \( x = -3 \)
• \( y = -2 \)

Step 2: Substitute the values to solve for \( k \)

Substitute \( x = -3 \) and \( y = -2 \) into the equation:

$$ (-3)(-2) = k $$

Multiply the two negative numbers. A negative number multiplied by another negative number results in a positive number:

$$ k = 6 $$

Answer:

6