Consider the equation y=2/5x+3y=2/5x+3

A line parallel to the above line would have a slope of   

A line perpendicular to the above line would have a slope of   

Given the equation \(y = \frac{2}{5}x + 3\):

1. **Slope of the original line**:  
   The slope of the line \(y = \frac{2}{5}x + 3\) is \(\frac{2}{5}\).

2. **Slope of a line parallel to the original line**:  
   A line parallel to this one will have the **same slope** as the original line, which is \(\frac{2}{5}\).

3. **Slope of a line perpendicular to the original line**:  
   A line perpendicular to the original line will have a slope that is the **negative reciprocal** of \(\frac{2}{5}\).  
   The negative reciprocal of \(\frac{2}{5}\) is \(-\frac{5}{2}\).

So:
- A line parallel to the original line would have a slope of \(\frac{2}{5}\).
- A line perpendicular to the original line would have a slope of \(-\frac{5}{2}\).

Would you like more details, or do you have any questions about this?

Here are 5 related questions to explore further:
1. How do you find the slope of a line from its equation in standard form?
2. What is the equation of a line parallel to \(y = \frac{2}{5}x + 3\) passing through the point \((1, 4)\)?
3. How do you find the equation of a line perpendicular to a given line that passes through a specific point?
4. What are the slopes of vertical and horizontal lines?
5. How does the slope-intercept form differ from the point-slope form in writing linear equations?

**Tip**: Always remember that parallel lines share the same slope, while perpendicular lines have slopes that are negative reciprocals of each other!

Explore the concept of slope in linear equations through examples. Learn how to find slopes of parallel and perpendicular lines using the equation y = (2/5)x + 3 as a guide. Suitable for Grades 7-9.

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