Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

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 was helpful. Please come back whenever you need more information or answers to your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.