Consider the line
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Slope of a perpendicular line:

To find the slope of the given line , we can rewrite it in slope-intercept form . Rearranging gives us , or . Thus, the slope is .

For a line parallel to this one, it will have the same slope: .

For a line perpendicular to this line, we take the negative reciprocal of the original slope. The negative reciprocal of is .

So, the slope of a perpendicular line is .

Now, for a fun fact: Did you know that the concept of parallel and perpendicular lines goes as far back as ancient Greece? Mathematicians like Euclid laid the foundational work, and it’s still vital for modern algebra and geometry!

Also, those negative reciprocals come in handy when working on geometry problems involving angles and intersections. By understanding these relationships, you can easily calculate angles of elevation or depression in real-world scenarios, like when designing ramps or analyzing construction plans.