Imagine you are a facilities manager for a logistics company reviewing the floor plan for a new warehouse. You need to ensure that two straight conveyor belt paths, represented by linear equations on the blueprint, are parallel so they never intersect. After converting both equations to slope-intercept form ($y = mx + b$), which of the following criteria must be met to confirm the lines are parallel?

Imagine you are a CAD technician reviewing the structural schematics of a new warehouse facility. You need to verify the alignment of various straight structural paths based on their linear equations. To correctly recall and apply the verification process for parallel lines, match each term or scenario with its corresponding rule.

A building contractor is verifying the alignment of two structural beams on a blueprint using their linear equations. To confirm that the beams are parallel and will never intersect, the contractor follows a standard verification process. Arrange the steps of this process in the correct order.

Electronic Schematic Alignment

A facilities manager is inspecting the floor plan of a warehouse to ensure two straight conveyor belts are parallel. If the linear equations for both belts have the exact same slope and the exact same $y$-intercept when written in the form $y = mx + b$, the belts are mathematically considered to be parallel.

As a CAD technician verifying the alignment of two structural beams on a blueprint, you convert their linear equations into slope-intercept form ($y = mx + b$). To confirm the beams are parallel, you must ensure that they possess different $y$-intercepts but share the exact same _____.