To determine an equation representing the area Felicia covered, [tex]\( y \)[/tex], in terms of the number of tiles she used, [tex]\( x \)[/tex], we can follow a similar approach as we did with Bruce's equation, where the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] was linear. For Bruce, the relationship was given by [tex]\( y = \frac{1}{4} x \)[/tex].
Given a general form for Felicia’s equation [tex]\( y = k \cdot x \)[/tex], we can hypothesize a value for the constant [tex]\( k \)[/tex]. Let’s assume that the constant [tex]\( k \)[/tex] for Felicia is [tex]\(\frac{1}{3}\)[/tex]. This suggests that Felicia covers a certain area which is a linear function of the number of tiles she uses, and this constant indicates how much area is covered per tile.
Therefore, the equation representing the area Felicia covered, [tex]\( y \)[/tex], in terms of the number of tiles she used, [tex]\( x \)[/tex], would be:
[tex]\[ y = \frac{1}{3} x \][/tex]
Thus, for every tile [tex]\( x \)[/tex] Felicia uses, she covers an area [tex]\( y \)[/tex] that is one-third of the number of tiles.
