Finding the Equation of a Line Perpendicular to $x = 4$ Through $(4, -5)$

A facility manager is using a coordinate system to plan a warehouse layout. A main support beam runs along the vertical line $x = 5$. A technician needs to install a secondary brace perpendicular to the main beam, passing through a mounting bracket located at the point $(3, -2)$. What is the equation of the line representing this secondary brace?

An architect is reviewing a digital site plan where a property boundary is marked by the vertical line $x = 5$. A new utility pipe must be laid perpendicular to this boundary, passing through an inspection hole at the coordinates $(3, -2)$. When drawing this pipe on the plan, it will be represented by a horizontal line with the equation $y = -2$.

A city planner is reviewing a grid-based map for a new park. A walking path follows the vertical line $x = 5$. A drainage pipe must be installed perpendicular to this path, passing through a maintenance hatch located at the point $(3, -2)$. Match each map feature with its corresponding geometric property.

An industrial floor manager is mapping out a new equipment layout on a coordinate grid. A main power conduit is represented by the vertical line $x = 5$. The manager needs to install a secondary safety rail perpendicular to the conduit that passes through a mounting bracket located at $(3, -2)$. Arrange the following steps in the correct order to graphically determine the equation of the safety rail.

Medical Imaging Grid Calibration

An agricultural mapping technician is programming a drone flight path over a rectangular crop field. A main vertical irrigation line runs along the line $x = 5$. The technician must program a perpendicular flight path that passes directly over a soil moisture sensor located at $(3, -2)$. Because the irrigation line is vertical, the perpendicular flight path must be completely horizontal. Graphically plotting this horizontal path through $(3, -2)$ reveals that every point along this line has a constant $y$-coordinate of ____.