A telecommunications technician is mapping a new fiber-optic cable that must be laid parallel to an existing line defined by the equation $y = 3x + 1$. The new cable must pass through a connection point located at (4, 2). To begin determining the equation for the new cable, which value from the given information must be identified as the slope ($m$)?

A land surveyor is mapping a new boundary line that must be parallel to an existing fence line represented by the equation $y = 3x + 1$. The new line must pass precisely through a survey marker located at ({}4, 2). Arrange the steps the surveyor must follow to determine the equation of the new line in slope-intercept form.

An interior designer is placing parallel decorative strips on a wall. The first strip follows the line $y = 3x + 1$, and the second strip must pass through the point (4, 2). To find the equation for the second strip, the designer should substitute 4 for the $y_1$ value and 2 for the $x_1$ value in the point-slope formula $y - y_1 = m(x - x_1)$.

Surveying Parallel Boundaries

Determining Parallel Slope for Solar Panel Rows

A network infrastructure planner is designing a new fiber-optic cable route that must run parallel to an existing main line represented by the equation $y = 3x + 1$. The new cable route must pass directly through a local distribution hub located at the coordinates ({}4, 2). To map the new route in the central system, the planner must enter its path in slope-intercept form, $y = mx + b$. Fill in the blank to complete the expression representing the right side of the equation for this new route: