the conversion of square feet to square yards can be represented by direct variation. three square yards are…

the conversion of square feet to square yards can be represented by direct variation. three square yards are equivalent to 27 square feet. let y represent the number of square yards and x the number of square feet. then y varies directly with x. what is the constant of variation? what is the equation representing the direct variation?

the conversion of square feet to square yards can be represented by direct variation. three square yards are equivalent to 27 square feet. let y represent the number of square yards and x the number of square feet. then y varies directly with x. what is the constant of variation? what is the equation representing the direct variation?

Answer

Explanation:

Step1: Recall direct - variation formula

The direct - variation formula is $y = kx$, where $k$ is the constant of variation.

Step2: Find the constant of variation

We know that when $y = 3$ (square yards) and $x = 27$ (square feet), we substitute these values into $y=kx$. So, $3=k\times27$. Solving for $k$, we get $k=\frac{3}{27}=\frac{1}{9}$.

Step3: Write the direct - variation equation

Substitute $k = \frac{1}{9}$ into $y = kx$. The equation is $y=\frac{1}{9}x$.

Answer:

The constant of variation is $\frac{1}{9}$. The equation representing the direct variation is $y=\frac{1}{9}x$.