Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To find the constant of variation [tex]\( k \)[/tex] for the direct variation equation [tex]\( y = kx \)[/tex] that passes through the point [tex]\((-3, 2)\)[/tex], we follow these steps:
1. Identify the given point:
- The given point is [tex]\((-3, 2)\)[/tex].
- This means when [tex]\( x = -3 \)[/tex], [tex]\( y = 2 \)[/tex].
2. Recall the direct variation formula:
- The formula for direct variation is [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of variation.
3. Substitute the values into the formula:
- Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = 2 \)[/tex] into the equation [tex]\( y = kx \)[/tex]:
[tex]\[ 2 = k \cdot (-3) \][/tex]
4. Solve for [tex]\( k \)[/tex]:
- Rearrange the equation to solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{y}{x} = \frac{2}{-3} \][/tex]
Therefore, the constant of variation [tex]\( k \)[/tex] is:
[tex]\[ k = -\frac{2}{3} \][/tex]
This value corresponds to one of the provided choices. So, the correct answer is:
[tex]\[ k = -\frac{2}{3} \][/tex]
1. Identify the given point:
- The given point is [tex]\((-3, 2)\)[/tex].
- This means when [tex]\( x = -3 \)[/tex], [tex]\( y = 2 \)[/tex].
2. Recall the direct variation formula:
- The formula for direct variation is [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of variation.
3. Substitute the values into the formula:
- Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = 2 \)[/tex] into the equation [tex]\( y = kx \)[/tex]:
[tex]\[ 2 = k \cdot (-3) \][/tex]
4. Solve for [tex]\( k \)[/tex]:
- Rearrange the equation to solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{y}{x} = \frac{2}{-3} \][/tex]
Therefore, the constant of variation [tex]\( k \)[/tex] is:
[tex]\[ k = -\frac{2}{3} \][/tex]
This value corresponds to one of the provided choices. So, the correct answer is:
[tex]\[ k = -\frac{2}{3} \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.