Question

The conversion of square feet to square yards can be represented by direct variation. Three square yards are

Answer 1

The constant of variation is $\frac{1}{9}$

The equation is $y=\frac{1}{9}x$

Solution:

Given that,

The conversion of square feet to square yards can be represented by direct variation

Let y represent the number of square yards

Let x be the number of square feet

$y \propto x$

y = kx ------ eqn 1

Where, "k" is the constant of variation

Three square yards are  equivalent to 27 square feet

Substitute, y = 3 and x = 27 in eqn 1

$3 = k \times 27\\\\k = \frac{3}{27}\\\\k = \frac{1}{9}$

Thus the constant of variation is $\frac{1}{9}$

What is the equation representing the direct variation?

Substitute k = 1/9 in eqn 1

$y = \frac{1}{9}x$

Thus the equation is found