Z varies directly with x and inversely with y when x=6 and y=2, z=15. How do you write the function that models each variation and then find z when x=4 and y=9?

Jun 13, 2015

You first find the constants of variation.

Explanation:

$z \leftrightarrow x$ and the constant=$A$
Direct variation means
$z = A \cdot x \to A = \frac{z}{x} = \frac{15}{6} = \frac{5}{2} \mathmr{and} 2.5$

$z \leftrightarrow y$ and the constant=$B$
Inverse variation means:
$y \cdot z = B \to B = 2 \cdot 15 = 30$