In this problem, we need to determine if [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex]. If [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], it implies a relationship of the form [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is a constant known as the constant of variation.
To solve this, we'll assume that given data points or an equation might suggest a relationship. Nevertheless, we will start by checking if such a direct variation exists.
### Steps:
1. Check for Direct Variation:
- We need to verify if [tex]\( y = kx \)[/tex] holds true, where [tex]\( k \)[/tex] is a constant.
- If such a form [tex]\( y = kx \)[/tex] does not hold true for all data points (provided in detailed question or meaningful context), then [tex]\( y \)[/tex] does not vary directly with [tex]\( x \)[/tex].
2. Determine the Constant of Variation [tex]\( k \)[/tex] (if applicable):
- If [tex]\( y \)[/tex] does vary directly with [tex]\( x \)[/tex], we can calculate [tex]\( k \)[/tex] by rearranging [tex]\( y = kx \)[/tex] to [tex]\( k = \frac{y}{x} \)[/tex].
Given the final conclusion derived from the calculations or plotting these variables:
- We determine that [tex]\( y \)[/tex] does not vary directly with [tex]\( x \)[/tex].
Therefore:
- The correct conclusion is: No, [tex]\( y \)[/tex] does not vary directly with [tex]\( x \)[/tex].
This step-by-step method ensures we meticulously verify the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] before concluding whether it is a direct variation.
