If x and y ar edirectly proportionate, when x=2 and x=3, what you’d be the value of x when y=9

If \(x\) and \(y\) are directly proportional, then we can express their relationship as:

\[ y = kx \]

where \(k\) is the constant of proportionality.

Given:
- When \(x = 2\), \(y = 6\)
- When \(x = 3\), \(y = 9\)

We need to find the value of \(y\) when \(x = 9\).

1. First, we find the constant of proportionality \(k\):
\[ y = kx \]
Using \(x = 2\) and \(y = 6\):
\[ 6 = k \cdot 2 \]
\[ k = \frac{6}{2} = 3 \]

Using \(x = 3\) and \(y = 9\) to verify \(k\):
\[ 9 = k \cdot 3 \]
\[ k = \frac{9}{3} = 3 \]

Since the constant \(k\) is consistent, we use it to find \(y\) when \(x = 9\):

\[ y = kx \]
\[ y = 3 \cdot 9 \]
\[ y = 27 \]

Therefore, the value of \(y\) when \(x = 9\) is \(27\).

Would you like more details or have any questions?

Here are 8 related questions for further practice:

1. If \(x\) and \(y\) are directly proportional and \(x = 5\) when \(y = 15\), what is the value of \(y\) when \(x = 8\)?
2. Given \(x\) and \(y\) are directly proportional, if \(x = 4\) and \(y = 10\), find \(y\) when \(x = 7\).
3. What is the constant of proportionality \(k\) if \(x = 2\) and \(y = 8\)?
4. If \(x\) is halved, what happens to \(y\) in a direct proportion relationship?
5. In a directly proportional relationship, if \(y = 20\) when \(x = 5\), what is \(x\) when \(y = 12\)?
6. How do you determine the constant of proportionality from a set of values?
7. Explain the difference between direct and inverse proportionality.
8. If \(x\) and \(y\) are directly proportional, and \(x = 10\) when \(y = 25\), find the value of \(y\) when \(x = 15\).

**Tip:** In a directly proportional relationship, as one variable increases, the other variable increases at a constant rate, and this rate is the constant of proportionality.

Explore the concept of direct proportionality with this math problem. Learn how to find the value of x when y = 9, given that x and y are directly proportional. Includes step-by-step solution and practice questions. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation