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Read the description of a proportional relationship. $\newline$ Neil measures the lengths of some objects in both yards and feet. There is a proportional relationship between the number of yards, $x$ , and the number of feet, $y$ . $\newline$ An object that is $2$ yards long is $6$ feet long. 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

Neil measures the lengths of some objects in both yards and feet. There is a proportional relationship between the number of yards,

x

, and the number of feet,

y

.

\newline

An object that is

2

yards long is

6

feet long. Write the equation for the relationship between

x

and

y

.

\newline

y =

____

Identify values: Step $1$ : Identify the given values. $\newline$ We know: $\newline$ Number of yards, $x = 2$ $\newline$ Number of feet, $y = 6$ $\newline$ What is the constant of proportionality, $k$ ? $\newline$ Constant of proportionality, $k = \frac{y}{x}$ $\newline$ $k = \frac{6}{2}$ $\newline$ $k = 3$
Write equation: Step $2$ : Write the equation for the proportional relationship using the constant of proportionality. $\newline$ Equation for proportional relationship: $y = kx$ $\newline$ $y = 3x$

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