i can solve probems using direction variation by

It sounds like you're asking about **direct variation** problems. Direct variation refers to a relationship between two variables where one variable is a constant multiple of the other. Mathematically, this is expressed as:

\[
y = kx
\]

where:
- \(y\) and \(x\) are the variables,
- \(k\) is the constant of variation, and
- \(x\) and \(y\) change together (i.e., as \(x\) increases, \(y\) increases proportionally).

### To solve direct variation problems, follow these steps:

1. **Identify the relationship**: Check if the problem describes a direct variation (it will typically say something like "y varies directly with x" or "y is directly proportional to x").

2. **Write the equation**: Use the formula \(y = kx\). If you know the constant of variation \(k\), you can directly substitute it into the equation.

3. **Find the constant of variation**: If given specific values of \(x\) and \(y\), substitute them into the equation to solve for \(k\). For example, if \(y = 6\) when \(x = 3\), you can solve for \(k\):
   \[
   6 = k \times 3 \quad \Rightarrow \quad k = \frac{6}{3} = 2
   \]

4. **Solve for unknowns**: After finding the constant \(k\), you can use the equation \(y = kx\) to find the value of \(y\) for a given \(x\), or vice versa.

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**Would you like an example problem to work through?** Or do you have a specific question about direct variation? Let me know if you'd like more details!

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Here are 5 follow-up questions related to direct variation:

1. How would you solve a problem where \(y = kx\) and you're given a new value for \(x\)?
2. What is the difference between direct variation and inverse variation?
3. How do you solve a real-world problem involving direct variation (e.g., speed and distance)?
4. Can you solve a direct variation problem without explicitly knowing \(k\)?
5. How can you interpret the constant of variation \(k\) in a practical context?

**Tip**: Always make sure you are given a clear indication that the relationship is a direct variation before applying \(y = kx\).

Learn how to solve direct variation problems using the equation y = kx, where y and x are variables that change proportionally. This guide provides clear steps to find the constant of variation k and solve for unknown values. Suitable for Grades 7-9 students.

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