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Read the description of a proportional relationship. $\newline$ Joy is hooked on a new book series, The Galaxy. Each book in the series is the same length and chronicles a different year in the Waka Waka Galaxy. Joy has cleared off the top shelf of her bookcase to leave room for each of the books as they come out. There is a proportional relationship between the number of books on the shelf, $x$ , and how much shelf space the books take up (in inches), $y$ . $\newline$ The first $3$ books in the series take up $6$ inches of space along the shelf. 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

Joy is hooked on a new book series, The Galaxy. Each book in the series is the same length and chronicles a different year in the Waka Waka Galaxy. Joy has cleared off the top shelf of her bookcase to leave room for each of the books as they come out. There is a proportional relationship between the number of books on the shelf,

x

, and how much shelf space the books take up (in inches),

y

.

\newline

The first

3

books in the series take up

6

inches of space along the shelf. Write the equation for the relationship between

x

and

y

.

\newline

y = \_\_

Identify Given Values: Step $1$ : Identify the given values and calculate the constant of proportionality, $k$ . $\newline$ Given: Number of books, $x = 3$ and shelf space, $y = 6$ . $\newline$ Calculate $k$ : $k = \frac{y}{x} = \frac{6}{3} = 2$
Calculate Constant of Proportionality: Step $2$ : Write the equation for the proportional relationship using the constant of proportionality. $\newline$ Since $k = 2$ , the equation is $y = kx$ . $\newline$ Thus, $y = 2x$

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