The equation you've provided is:

\[
y = \frac{x}{k}
\]

This is a simple linear equation, where:

- \(y\) is the dependent variable.
- \(x\) is the independent variable.
- \(k\) is a constant (non-zero to avoid division by zero).

The equation shows that \(y\) is directly proportional to \(x\) and inversely proportional to the constant \(k\). If \(k > 0\), as \(x\) increases, \(y\) also increases, and if \(x\) decreases, \(y\) decreases.

### Key Points:
1. As \(k\) becomes larger, the slope of the line becomes shallower (smaller slope).
2. If \(k\) is negative, \(y\) and \(x\) have an inverse relationship.
3. The equation represents a straight line passing through the origin with slope \( \frac{1}{k} \).

Would you like more details on this or an example of how to apply this equation?

### Further Questions:
1. What happens when \(k\) approaches zero?
2. How would you graph this equation for different values of \(k\)?
3. What is the slope of the line represented by this equation?
4. How would you solve for \(x\) if \(y\) and \(k\) are given?
5. What changes if \(k\) is negative?

### Tip:
In this form, the equation resembles a proportional relationship, where \(x\) is directly proportional to \(y\) if \(k\) is constant.

Explore the linear equation y = x/k and learn how y is directly proportional to x and inversely proportional to k. Understand key concepts such as proportionality, slope, and how changing the value of k affects the relationship between x and y. Suitable for students in Grades 8-10.

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