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Read the description of a proportional relationship. $\newline$ There's a huge sale at the grocery store, so Carla stocks up on her favorite breakfast cereal, Frosted Crunchy Bunches. As she puts the cereal boxes on a shelf in her pantry, she wonders if she has enough shelf space. There is a proportional relationship between the number of cereal boxes Carla stores on her pantry shelf, $x$ , and the amount of shelf space (in inches) the boxes take up, $y$ . $\newline$ Storing $3$ boxes takes up $12$ inches of shelf space. 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

There's a huge sale at the grocery store, so Carla stocks up on her favorite breakfast cereal, Frosted Crunchy Bunches. As she puts the cereal boxes on a shelf in her pantry, she wonders if she has enough shelf space. There is a proportional relationship between the number of cereal boxes Carla stores on her pantry shelf,

x

, and the amount of shelf space (in inches) the boxes take up,

y

.

\newline

Storing

3

boxes takes up

12

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

x

and

y

.

\newline

y = \_\_\_

Identify Values: Identify the given values: $\newline$ Number of cereal boxes, $x = 3$ $\newline$ Shelf space occupied, $y = 12$ $\newline$ Calculate the constant of proportionality, $k$ . $\newline$ $k = \frac{y}{x}$ $\newline$ $k = \frac{12}{3}$ $\newline$ $k = 4$
Calculate Constant: Use the constant of proportionality to write the equation. $\newline$ Since $k = 4$ , the equation for the proportional relationship is: $\newline$ $y = kx$ $\newline$ $y = 4x$

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