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?

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

Let

x -----> the number of square feet

y -----> the number of square yards

Three square yards are equivalent to 27 square feet

so

we have the point (27,3)

Part 1) What is the constant of variation?

The constant of variation or proportionality is equal to

[tex]k=y/x[/tex]

substitute the values

[tex]k=3/27[/tex]

Simplify

[tex]k=1/9[/tex]

Part 2) What is the equation representing the direct variation?

we know that

[tex]y=kx[/tex]

substitute the value of k

[tex]y=\frac{1}{9}x[/tex]

ewomazinoade ewomazinoade · Answer 2 · 2022-02-07T13:54:13+01:00

The constant of variation is 1/9.

The equation representing direct proportion is 3 yards² = k27ft²

What is the equation that represents direct proportionality?

The equation that can be used to represent direct proportion is y = kx

Where:

y = independent variable
k = constant of proportionality
x = independent variable

3 yards² = k27ft²

k = 3 /27 = 1/9.

To learn more about direct proportion, please check: brainly.com/question/12237076