Question
What is an equation of the line that passes through the point
Ask by Christensen Ryan. in the United States
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the line is
Solution
To find the equation of the line that passes through the point
-
Find the slope of the given line:First, rewrite the equation
in slope-intercept form ( ) to identify its slope. So, the slope () of the given line is 2. -
Determine the slope of the perpendicular line:The slope of a line perpendicular to another is the negative reciprocal of the original slope. Therefore:So, the slope (
) of the perpendicular line is . -
Use the point-slope form to find the equation:The point-slope form of a line is:Plugging in the point
and the slope : Simplifying:So, the equation of the desired line in slope-intercept form is:
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Simplify this solution Bonus Knowledge
To find the equation of a line that is perpendicular to the line
The slope of a line that is perpendicular to this would be the negative reciprocal, which is
This simplifies to:
resulting in:
This is the equation of the required line!
Now, here’s a bit of fun history: Did you know that the concept of perpendicular lines has its roots in the work of ancient Greek mathematicians? Euclid’s “Elements” laid down the foundational rules of geometry, establishing the relationship between angles and lines.
Moreover, perpendicular lines aren’t just a mathematical curiosity; they’re everywhere in real life! For example, think about road designs or the way buildings are constructed. Architects and engineers use perpendicular lines to create stable and efficient structures, ensuring that everything stands straight and sturdy!
