Question

two quantities x and y vary inversely, and y = 18 when x = 3.
part a
write an equation for the relationship between x and y.
a. equation:

part b.
if x = 6, what is the value of y?
b. y =

Explanation:

Step1: Recall inverse variation formula

Inverse variation is defined as $y = \frac{k}{x}$, where $k$ is the constant of variation.

Step2: Solve for constant $k$

Substitute $x=3$, $y=18$ into the formula:
$18 = \frac{k}{3}$
Multiply both sides by 3: $k = 18 \times 3 = 54$

Step3: Write the inverse variation equation

Substitute $k=54$ back into $y = \frac{k}{x}$:
$y = \frac{54}{x}$

Step4: Find $y$ when $x=6$

Substitute $x=6$ into $y = \frac{54}{x}$:
$y = \frac{54}{6} = 9$

Answer:

Part A: $y = \frac{54}{x}$
Part B: $9$