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Read the description of a proportional relationship. $\newline$ Dana is finding the perimeter of different-sized squares. There is a proportional relationship between the side length of the square in inches, $x$ , and the perimeter of the square in inches, $y$ . $\newline$ A square with $2$ -inch side lengths has a perimeter of $8$ inches. 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

Dana is finding the perimeter of different-sized squares. There is a proportional relationship between the side length of the square in inches,

x

, and the perimeter of the square in inches,

y

.

\newline

A square with

2

-inch side lengths has a perimeter of

8

inches. Write the equation for the relationship between

x

and

y

.

\newline

y =

____

Identify Given Values: Step $1$ : Identify the given values. $\newline$ We know the side length of the square, $x = 2$ inches, and the perimeter, $y = 8$ inches. We need to find the constant of proportionality, $k$ .
Calculate Constant of Proportionality: Step $2$ : Calculate the constant of proportionality, $k$ . Using the formula $k = \frac{y}{x}$ , we calculate: $k = \frac{8}{2}$ $k = 4$
Write Proportional Relationship Equation: Step $3$ : Write the equation for the proportional relationship. $\newline$ Since the perimeter of a square is calculated as $y = 4x$ , where $x$ is the side length, we use the constant of proportionality found in Step $2$ . $\newline$ $y = 4x$

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