Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Determine whether or not the equations represent a direct variation. Sort the equations into the appropriate category.

1. [tex]\( x = -1 \)[/tex]
2. [tex]\( y = \left( \frac{2}{7} \right) x \)[/tex]
3. [tex]\( -0.5x = y \)[/tex]
4. [tex]\( y = 2.2x + 7 \)[/tex]
5. [tex]\( y = 4 \)[/tex]

Sagot :

GinnyAnswer
To determine whether the given equations represent a direct variation, we need to understand what direct variation means. Direct variation implies a relationship of the form [tex]\( y = kx \)[/tex] or [tex]\( x = ky \)[/tex], where [tex]\( k \)[/tex] is a constant.

Let's analyze each given equation step-by-step:

1. [tex]\( x = -1 \)[/tex]:
- This equation states that [tex]\( x \)[/tex] is always equal to [tex]\(-1\)[/tex], regardless of [tex]\( y \)[/tex]. This is not in the form [tex]\( y = kx \)[/tex] or [tex]\( x = ky \)[/tex], so it does not represent a direct variation.

2. [tex]\( y = \left(\frac{2}{7}\right) x \)[/tex]:
- This equation is of the form [tex]\( y = kx \)[/tex], where [tex]\( k = \frac{2}{7} \)[/tex]. This is a direct variation with [tex]\( k = \frac{2}{7} \)[/tex].

3. [tex]\( -0.5 x = y \)[/tex]:
- This equation can be rewritten as [tex]\( y = -0.5x \)[/tex], which is of the form [tex]\( y = kx \)[/tex] with [tex]\( k = -0.5 \)[/tex]. Therefore, this is a direct variation with [tex]\( k = -0.5 \)[/tex].

4. [tex]\( y = 2.2 x + 7 \)[/tex]:
- This equation includes an additional constant [tex]\(+7\)[/tex]. Therefore, it cannot be written in the form [tex]\( y = kx \)[/tex] because of the additional term. This is not a direct variation.

5. [tex]\( y = 4 \)[/tex]:
- This equation states that [tex]\( y \)[/tex] is always equal to 4, regardless of [tex]\( x \)[/tex]. This does not fit the form [tex]\( y = kx \)[/tex] or [tex]\( x = ky \)[/tex], so it is not a direct variation.

Now, I'll categorize the equations based on whether they represent direct variation or not.

Direct Variation:
- [tex]\( y = \left(\frac{2}{7}\right) x \)[/tex]
- [tex]\( -0.5 x = y \)[/tex]

Not Direct Variation:
- [tex]\( x = -1 \)[/tex]
- [tex]\( y = 2.2 x + 7 \)[/tex]
- [tex]\( y = 4 \)[/tex]

So, the complete sorted categories are:

- Direct Variation: [tex]\( y = \left(\frac{2}{7}\right) x \)[/tex], [tex]\( -0.5 x = y \)[/tex]
- Not Direct Variation: [tex]\( x = -1 \)[/tex], [tex]\( y = 2.2 x + 7 \)[/tex], [tex]\( y = 4 \)[/tex]
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.