A logistics technician is planning a new conveyor belt path in a warehouse. The new path must be parallel to an existing line represented by the equation $y = \frac{1}{2}x - 3$ and must pass through a specific loading dock located at the coordinates (6, 4). Arrange the following steps in the correct order to determine the final algebraic equation for the new path.

A structural drafter is modeling a new support beam that must run perfectly parallel to an existing beam. The existing beam lies on the line $y = \frac{1}{2}x - 3$, and the new beam must pass exactly through the anchor point (6, 4). To construct the algebraic equation for the new beam, the drafter must recall the point-slope form and substitute the correct values. Which of the following represents the correct initial setup for the new beam's equation?

A manufacturing technician is programming a laser cutter to create two parallel paths on a metal sheet. The first path is modeled by the equation $y = \frac{1}{2}x - 3$. The second path must be perfectly parallel to the first and pass through an alignment point located at (6, 4). To begin calculating the equation for the second path, match each mathematical component with its correct numerical value from this scenario.

Recalling Parallel Slope Properties in Infrastructure Planning

A network technician is laying a new fiber optic cable parallel to an existing line represented by the equation $y = \frac{1}{2}x - 3$. To construct the algebraic equation for the new cable path passing through the point (6, 4), the technician correctly assumes that the slope of the new line must be $\frac{1}{2}$. Is this assumption correct?

A logistics coordinator is mapping out a new automated guided vehicle (AGV) path on the warehouse floor. This new path must run perfectly parallel to an existing track modeled by the equation $y = \frac{1}{2}x - 3$ and pass through a specific charging station at the coordinates (6, 4). To construct the algebraic equation for this new path, the coordinator must recall the rule for parallel slopes. Since the new path is parallel to the existing one, the slope ($m$) of the new path must be ____.