https://file.aiquickdraw.com/mathbot/file/1726535980598wsuh91yu.jpg

Let's analyze the question based on the provided image.

1. **Given equation of the line**: 
   \[
   y = \frac{2}{3}x
   \]
   This is a linear equation in slope-intercept form, \(y = mx + b\), where \(m\) is the slope. In this case, the slope \(m\) of the line is \(\frac{2}{3}\).

2. **Slope of a line parallel to this line**: 
   The slope of any line that is parallel to another line is the same as the slope of the original line. Therefore, the slope of a line parallel to \(y = \frac{2}{3}x\) is also:
   \[
   \frac{2}{3}
   \]

3. **Slope of a line perpendicular to this line**: 
   The slope of a line that is perpendicular to another line is the negative reciprocal of the slope of the original line. So, the negative reciprocal of \(\frac{2}{3}\) is:
   \[
   -\frac{3}{2}
   \]

### Final Answer:
- Slope of a parallel line: \(\frac{2}{3}\)
- Slope of a perpendicular line: \(-\frac{3}{2}\)

Would you like further details or explanations? Here are 5 related questions for more practice:

1. What is the slope of a line parallel to \(y = -\frac{4}{5}x + 2\)?
2. How do you find the equation of a line given a point and a slope?
3. If a line has a slope of 1, what is the slope of a line perpendicular to it?
4. What is the general form of a linear equation, and how can you identify the slope from it?
5. Can two lines with different y-intercepts be parallel?

**Tip**: To find the slope of a perpendicular line, always take the negative reciprocal of the original slope!

Consider the line y = 2/3x. What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?

Learn how to determine the slope of a line parallel and perpendicular to y = 2/3x. This problem covers linear equations and the relationship between parallel and perpendicular slopes. Suitable for students in Grades 8-10.

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