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 $y = kx$.