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If [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex], and [tex]\( y \)[/tex] is 48 when [tex]\( x \)[/tex] is 6, which expression can be used to find the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 2?

A. [tex]\( y = \frac{48}{6}(2) \)[/tex]

B. [tex]\( y = \frac{6}{48}(2) \)[/tex]

C. [tex]\( y = \frac{(48)(8)}{2} \)[/tex]

D. [tex]\( y = \frac{2}{(48)(6)} \)[/tex]



Answer :

GinnyAnswer
To solve the problem where [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex], we start by understanding that the relationship can be expressed using the formula [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is a constant of variation.

Given:
- [tex]\( y = 48 \)[/tex] when [tex]\( x = 6 \)[/tex]

First, we find the constant [tex]\( k \)[/tex] by substituting the given values into the formula [tex]\( y = kx \)[/tex].

[tex]\[ 48 = k \cdot 6 \][/tex]

Solving for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{48}{6} \][/tex]

Now we have the value of [tex]\( k \)[/tex]. To find the value of [tex]\( y \)[/tex] when [tex]\( x = 2 \)[/tex], we use the same direct variation formula [tex]\( y = kx \)[/tex]:

[tex]\[ y = \left(\frac{48}{6}\right) \cdot 2 \][/tex]

Simplifying the expression inside the parentheses:

[tex]\[ y = \frac{48}{6} \cdot 2 = 8 \cdot 2 = 16 \][/tex]

So, the correct expression to find the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is [tex]\( 2 \)[/tex] is:

[tex]\[ y = \frac{48}{6} (2) \][/tex]

Therefore, the correct option is:

[tex]\[ y = \frac{48}{6} (2) \][/tex]

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