Question

for the inverse variation equation $xy = k$, what is the constant of variation, $k$, when $x = -2$ and $y = 5$? $-\frac{2}{5}$, $-10$, $\frac{5}{2}$, $10$

Explanation:

Step1: Identify the formula

The inverse variation equation is given as \( xy = k \). We need to find \( k \) when \( x = -2 \) and \( y = 5 \).

Step2: Substitute the values

Substitute \( x = -2 \) and \( y = 5 \) into the equation \( xy = k \). So we have \( (-2) \times 5 = k \).

Step3: Calculate the product

Calculate \( (-2) \times 5 \). Multiplying a negative number and a positive number gives a negative result, so \( (-2) \times 5 = -10 \). Thus, \( k = -10 \).

Answer:

\( -10 \) (corresponding to the option with value -10)