Example

Finding the Equation of a Line Perpendicular to x=5x = 5 Through (3,2)(3, -2)

To formulate the equation of a line perpendicular to x=5x = 5 mapping cleanly through the point (3,2)(3, -2), leverage fundamental orthogonal relationships. The starting line, x=5x = 5, constitutes a strictly vertical plot. Because perpendicular interactions strictly flip orientation, a vertical baseline forms a horizontal perpendicular counterpart, establishing an absolute slope of m=0m_{\perp} = 0. Inserting the given geometric coordinates (x1,y1)=(3,2)(x_1, y_1) = (3, -2) and the zero slope solidly into the standard point-slope architecture, yy1=m(xx1)y - y_1 = m(x - x_1), yields y(2)=0(x3)y - (-2) = 0(x - 3). Simplifying the right-side parentheses entirely to zero leaves y+2=0y + 2 = 0, which then neatly resolves exactly to the finalized horizontal structure of y=2y = -2. This algebraic process confirms the unique geometric constraint that strictly dictates the constant yy-coordinate.

Image 0

0

1

Updated 2026-04-23

Contributors are:

Who are from:

Tags

OpenStax

Elementary Algebra @ OpenStax

Ch.4 Graphs - Elementary Algebra @ OpenStax

Algebra

Math

Prealgebra

Intermediate Algebra @ OpenStax

Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax

Related
Learn After