Understanding the Slope of a Perpendicular Line: A Comprehensive Guide for SEO Optimization

When dealing with lines in the coordinate plane, understanding the relationship between their slopes is crucial. This article will delve into the specific scenario where we need to determine the slope of a line that is perpendicular to another line, with a given equation. We will use the equation -2y -8x - 9 as an example to illustrate the process.

Given Line and Its Slope

The equation provided is:

-2y -8x - 9

To find the slope of the line, we need to rewrite the equation in the slope-intercept form, which is y mx b, where m is the slope and b is the y-intercept. Let's start by isolating y on one side of the equation.

Divide the entire equation by -2:

y  4x - frac{9}{2}

From this equation, we can see that the slope m of the given line is 4.

Slope of a Perpendicular Line

The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. This means that if the slope of one line is m, the slope of the line perpendicular to it is -frac{1}{m}.

The slope m of the given line is 4. Therefore, the slope of the line perpendicular to it is:

text{Slope of the perpendicular line}  -frac{1}{4}

Thus, the slope of the line perpendicular to the given line is -frac{1}{4}.

Product of Slopes of Perpendicular Lines

Another important relationship to remember is that the product of the slopes of two perpendicular lines is always -1. This can be written as:

(text{Slope of line 1} times text{Slope of line 2} -1)

In our specific example:

(text{Slope of given line (4)} times text{Slope of perpendicular line} (text{-}frac{1}{4}) -1)

This relationship is crucial for verifying the calculation and understanding the geometric properties of lines.

SEO Considerations

When optimizing this content for search engines, it's important to include relevant keywords such as 'slope of a line,' 'perpendicular line,' and 'slope-intercept form.'

Make sure to use these keywords naturally within your content, headings, and meta descriptions. This will help improve the visibility of your article in search results and attract more organic traffic.

Incorporating images, diagrams, and examples will also enhance the reader's understanding and engagement with the content. Properly structured headings (H1, H2, H3) will guide the search engines to comprehend the structure and importance of the content.

Finally, ensure that the content is accessible, providing an educational value and a clear, concise explanation of the concept, making it a valuable resource for students and professionals alike.