The equation given is:

\[
y = \frac{2}{3}x
\]

This is a linear equation, where the slope (m) of the line is \(\frac{2}{3}\) and the y-intercept is 0, meaning the line passes through the origin \((0, 0)\).

### Key characteristics:
1. **Slope (m)**: The slope is \(\frac{2}{3}\), which means for every 3 units you move horizontally to the right (along the x-axis), the line moves up by 2 units (along the y-axis).
2. **Y-Intercept (b)**: Since there is no constant term, the y-intercept is 0.
3. **Line Equation Form**: The equation is in slope-intercept form \(y = mx + b\), where \(m = \frac{2}{3}\) and \(b = 0\).

### Graphing:
- Start at the origin \((0,0)\).
- Use the slope to find another point. For instance, from \((0,0)\), move 3 units to the right and 2 units up to plot the point \((3,2)\).
- Draw a straight line through these points.

Would you like more details on how to graph this equation, or do you have other questions?

### Follow-up Questions:
1. How would the graph change if the slope was negative, say \(-\frac{2}{3}\)?
2. What happens to the line if we add a y-intercept, like \(y = \frac{2}{3}x + 4\)?
3. Can you determine the x-intercept of this line?
4. How would the equation change if the slope were steeper, say \(y = 2x\)?
5. Can you find the equation of a line parallel to this one but passing through \((0, 5)\)?

### Tip:
When working with slopes, remember that the sign of the slope determines the direction of the line: positive slopes rise to the right, while negative slopes fall to the right.

Explore the linear equation y = (2/3)x, focusing on the slope-intercept form. Learn how to graph the equation, identify the slope and y-intercept, and understand its characteristics. This guide is ideal for students in Grades 6-8 looking to deepen their understanding of linear functions.

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