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Read the description of a proportional relationship. $\newline$ Clara owns and operates Stain-B-Gone Carpet Cleaners. She uses a special non-toxic cleaning solution to clean carpets. There is a proportional relationship between the amount of cleaning solution (in quarts) Clara uses, $x$ , and the area of carpet (in square yards) she cleans with the solution, $y$ . $\newline$ Clara uses $3$ quarts of cleaning solution to clean $12$ square yards of carpet. Write the equation for the relationship between $x$ and $y$ . $\newline$ $y = \_$

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Write and solve equations for proportional relationships

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Q. Read the description of a proportional relationship.

\newline

Clara owns and operates Stain-B-Gone Carpet Cleaners. She uses a special non-toxic cleaning solution to clean carpets. There is a proportional relationship between the amount of cleaning solution (in quarts) Clara uses,

x

, and the area of carpet (in square yards) she cleans with the solution,

y

.

\newline

Clara uses

3

quarts of cleaning solution to clean

12

square yards of carpet. Write the equation for the relationship between

x

and

y

.

\newline

y = \_

Identify Given Values: Step $1$ : Identify the given values and the constant of proportionality, $k$ . $\newline$ Given: $x = 3$ quarts of cleaning solution, $y = 12$ square yards of carpet. $\newline$ Calculate $k$ as $k = \frac{y}{x}$ . $\newline$ $k = \frac{12}{3}$ $\newline$ $k = 4$
Calculate Constant of Proportionality: Step $2$ : Write the equation for the proportional relationship using the constant of proportionality. $\newline$ Since $k = 4$ , the equation is $y = kx$ . $\newline$ Thus, $y = 4x$ .

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