representing direct variation with an equation\nthe conversion of square feet to square yards can be…

representing direct variation with an equation\nthe 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.\nwhat is the constant of variation?\nwhat is the equation representing the direct variation?

representing direct variation with an equation\nthe 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.\nwhat is the constant of variation?\nwhat 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

Substituting $k = \frac{1}{9}$ into $y = kx$, the equation is $y=\frac{1}{9}x$.

Answer:

Constant of variation: $\frac{1}{9}$ Equation: $y=\frac{1}{9}x$