Question

Y is inversely proportional to x.

Answer 1

Answer:

1. $xy = 63$

2. $y = 3$

Step-by-step explanation:

Given

Variation: inverse Proportion

y = 7, x = 9

Required

- Write an equation connecting y and x

- Find y when x = 21

Given that thee variation is inversely proportional;

This implies that

$y\ \alpha\ \frac{1}{x}$

Convert variation to equation

$y\ = \frac{k}{x}$ ----------- Equation 1

Where k is the constant of variation

Substitute 7 for y and 9 for x in equation 1

$7 = \frac{k}{9}$

Multiply both sides by 9

$9 * 7 = 9 * \frac{k}{9}$

$63 = k$

Substitute 63 for k in equation 1

$y = \frac{63}{x}$

Multiply both sides by x

$x * y = \frac{63}{x} * x$

$xy = 63$

Hence, the equation connecting x and y is $xy = 63$

Solving for when x = 21

Substitute 21 for x in the above equation

$21 * y = 63$

Divide both sides by 21

$\frac{21 * y}{21} = \frac{63}{21}$

$y = 3$