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In this activity, you will use equations and graphs to represent real-world relationships and use them to draw conclusions about the relationships.

The tiles that Bruce used were each [tex]\(\frac{1}{4}\)[/tex] of a square foot in area. The table shows the area covered by Felicia's tiles in terms of the number of tiles used.
\begin{tabular}{|c|c|}
\hline Number of Tiles & Area Covered (sq ft) \\
\hline 6 & 1 \\
\hline 12 & 2 \\
\hline 18 & 3 \\
\hline
\end{tabular}

Bruce and Felicia want to know whose tiles cover the most area per tile.

Part A

Write an equation representing the area Bruce covered, [tex]\(y\)[/tex], in terms of the number of tiles he used, [tex]\(x\)[/tex].

[tex]\[ y = \][/tex]

Sagot :

GinnyAnsweridn
To find the equation representing the area [tex]\( y \)[/tex] that Bruce covered in terms of the number of tiles he used, [tex]\( x \)[/tex], let's break down the relationship between the number of tiles and the area covered.

We know that each of Bruce's tiles covers an area of [tex]\(\frac{1}{4}\)[/tex] square foot.

To express this relationship mathematically:

1. Let [tex]\( x \)[/tex] be the number of tiles Bruce used.
2. Since each tile covers [tex]\(\frac{1}{4}\)[/tex] square foot, the total area [tex]\( y \)[/tex] covered by [tex]\( x \)[/tex] tiles can be calculated by multiplying [tex]\( x \)[/tex] by [tex]\(\frac{1}{4}\)[/tex].

Thus, the equation that represents the area [tex]\( y \)[/tex] covered by Bruce in terms of the number of tiles [tex]\( x \)[/tex] he used is:

[tex]\[ y = \frac{x}{4} \][/tex]

This equation shows that the total area covered, [tex]\( y \)[/tex], is directly proportional to the number of tiles used, [tex]\( x \)[/tex], with each tile contributing [tex]\(\frac{1}{4}\)[/tex] square foot to the total area.
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