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Read the description of a proportional relationship. $\newline$ Over the summer, Belleville Science Academy renovates its building. The academy's principal hires Aubrey to lay new tile in the main hallway. There is a proportional relationship between the length (in feet) of hallway Aubrey covers with tiles, $x$ , and the number of tiles she needs, $y$ . $\newline$ To cover the first $2$ feet of the hallway, Aubrey needs $8$ tiles. 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

Over the summer, Belleville Science Academy renovates its building. The academy's principal hires Aubrey to lay new tile in the main hallway. There is a proportional relationship between the length (in feet) of hallway Aubrey covers with tiles,

x

, and the number of tiles she needs,

y

.

\newline

To cover the first

2

feet of the hallway, Aubrey needs

8

tiles. Write the equation for the relationship between

x

and

y

.

\newline

y = \_\_

Identify Given Values: Step $1$ : Identify the given values. $\newline$ Length covered by Aubrey, $x = 2$ feet. $\newline$ Number of tiles used, $y = 8$ . $\newline$ Calculate the constant of proportionality, $k$ . $\newline$ $k = \frac{y}{x}$ $\newline$ $k = \frac{8}{2}$ $\newline$ $k = 4$
Calculate Constant of Proportionality: Step $2$ : Write the equation using the constant of proportionality. $\newline$ Since $k = 4$ , the equation for the proportional relationship is: $\newline$ $y = kx$ $\newline$ $y = 4x$

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