MHB Finding lines through given point perpendicular and parallel to given line

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To find the equations of lines parallel and perpendicular to y = 2x + 3 that pass through the point (1, 1), the point-slope form is used. The parallel line shares the same slope of 2, resulting in the equation y - 1 = 2(x - 1). For the perpendicular line, the slope is the opposite reciprocal, -1/2, leading to the equation y - 1 = -1/2(x - 1). The discussion emphasizes the correct categorization of the topic within Pre-algebra and Algebra rather than Linear and Abstract algebra. Understanding these concepts is essential for solving similar problems.
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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