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.
