Finding lines through given point perpendicular and parallel to given line

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SUMMARY

The discussion focuses on finding the equations of lines that are both perpendicular and parallel to the line represented by the equation y = 2x + 3, specifically through the point (1, 1). The point-slope form of a line, expressed as y - y1 = m(x - x1), is utilized to derive the equations. The parallel line maintains the same slope of 2, resulting in the equation y - 1 = 2(x - 1). Conversely, the perpendicular line has a slope of -1/2, leading to the equation y - 1 = -1/2(x - 1). The discussion emphasizes the appropriate categorization of the topic within Pre-algebra and Algebra.

PREREQUISITES
  • Understanding of point-slope form of a line
  • Knowledge of slope concepts, including parallel and perpendicular lines
  • Familiarity with linear equations
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the point-slope form of linear equations in detail
  • Learn about the properties of slopes for parallel and perpendicular lines
  • Practice deriving equations of lines from given points and slopes
  • Explore applications of linear equations in real-world scenarios
USEFUL FOR

Students in Pre-algebra and Algebra courses, educators teaching linear equations, and anyone seeking to enhance their understanding of geometric relationships between lines.

swag312
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Hey, not sure how to translate this from my native language, I hope you understand what I mean.

Write down for the line
y = 2x + 3 perpendicular and parallel lines passing through the point
(1; 1) equations.
 
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swag312 said:
Hey, not sure how to translate this from my native language, I hope you understand what I mean.

Write down for the line
y = 2x + 3 perpendicular and parallel lines passing through the point
(1; 1) equations.

using the point-slope form, $y-y_1 = m(x-x_1)$

parallel lines have the same slope ...

$y-1 = 2(x-1)$

perpendicular lines have slopes that are opposite reciprocals ...

$y - 1 = -\dfrac{1}{2}(x-1)$

... and this post belongs in Pre-algebra and Algebra, not Linear and Abstract algebra
 

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