Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To determine the relationship between [tex]\(y\)[/tex] and [tex]\(x\)[/tex], we start by recognizing that since [tex]\(y\)[/tex] and [tex]\(x\)[/tex] are in direct proportion, their relationship can be expressed as [tex]\(y = kx\)[/tex], where [tex]\(k\)[/tex] is a proportionality constant.
Given:
- [tex]\(x_1 = 3\)[/tex]
- [tex]\(x_2 = 8\)[/tex]
- Difference in [tex]\(y\)[/tex] values when [tex]\(x = 3\)[/tex] and [tex]\(x = 8\)[/tex] is 20.
This piece of information can be mathematically represented as:
[tex]\[ y_2 - y_1 = 20 \][/tex]
where [tex]\(y_1\)[/tex] and [tex]\(y_2\)[/tex] are the corresponding [tex]\(y\)[/tex] values for [tex]\(x_1\)[/tex] and [tex]\(x_2\)[/tex].
Since [tex]\(y\)[/tex] is directly proportional to [tex]\(x\)[/tex],
[tex]\[ y_1 = k x_1 \][/tex]
[tex]\[ y_2 = k x_2 \][/tex]
Therefore,
[tex]\[ y_2 - y_1 = k x_2 - k x_1 \][/tex]
[tex]\[ 20 = k x_2 - k x_1 \][/tex]
[tex]\[ 20 = k (x_2 - x_1) \][/tex]
Substituting the given values of [tex]\(x_1\)[/tex] and [tex]\(x_2\)[/tex]:
[tex]\[ 20 = k (8 - 3) \][/tex]
[tex]\[ 20 = k (5) \][/tex]
Solving for [tex]\(k\)[/tex]:
[tex]\[ k = \frac{20}{5} = 4.0 \][/tex]
Now that we have determined the proportionality constant [tex]\(k = 4.0\)[/tex], we can express [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex]:
[tex]\[ y = 4.0 x \][/tex]
Therefore, the equation representing [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex] is:
[tex]\[ y = 4.0 x \][/tex]
Given:
- [tex]\(x_1 = 3\)[/tex]
- [tex]\(x_2 = 8\)[/tex]
- Difference in [tex]\(y\)[/tex] values when [tex]\(x = 3\)[/tex] and [tex]\(x = 8\)[/tex] is 20.
This piece of information can be mathematically represented as:
[tex]\[ y_2 - y_1 = 20 \][/tex]
where [tex]\(y_1\)[/tex] and [tex]\(y_2\)[/tex] are the corresponding [tex]\(y\)[/tex] values for [tex]\(x_1\)[/tex] and [tex]\(x_2\)[/tex].
Since [tex]\(y\)[/tex] is directly proportional to [tex]\(x\)[/tex],
[tex]\[ y_1 = k x_1 \][/tex]
[tex]\[ y_2 = k x_2 \][/tex]
Therefore,
[tex]\[ y_2 - y_1 = k x_2 - k x_1 \][/tex]
[tex]\[ 20 = k x_2 - k x_1 \][/tex]
[tex]\[ 20 = k (x_2 - x_1) \][/tex]
Substituting the given values of [tex]\(x_1\)[/tex] and [tex]\(x_2\)[/tex]:
[tex]\[ 20 = k (8 - 3) \][/tex]
[tex]\[ 20 = k (5) \][/tex]
Solving for [tex]\(k\)[/tex]:
[tex]\[ k = \frac{20}{5} = 4.0 \][/tex]
Now that we have determined the proportionality constant [tex]\(k = 4.0\)[/tex], we can express [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex]:
[tex]\[ y = 4.0 x \][/tex]
Therefore, the equation representing [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex] is:
[tex]\[ y = 4.0 x \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.