Essay

Documenting Path Alignment Formulas for Utility Infrastructure

As an apprentice field surveyor, you are drafting a technical report to document the layout of a straight fiber-optic cable line on a project grid. The cable runs along a linear trajectory directly between two key connection hubs located at coordinates (2,4)(-2, -4) and (1,3)(1, -3). Your supervisor has requested that you write a clear, step-by-step mathematical explanation of how you manually find the path's equation in slope-intercept form (y=mx+by = mx + b).

In your report, write an essay outlining the complete 'two-points procedure' to find this line's equation. To satisfy your supervisor's documentation standards, you must explicitly:

  1. State the slope formula and show how to calculate the slope (mm) using the points (2,4)(-2, -4) and (1,3)(1, -3), explaining the sign changes that occur when subtracting negative numbers.
  2. State the point-slope formula, yy1=m(xx1)y - y_1 = m(x - x_1), and show the initial equation after substituting your calculated slope and the point (1,3)(1, -3).
  3. Detail the subsequent algebraic manipulations needed to simplify the equation, distribute the fractional slope, and subtract 3 from both sides using a common denominator to arrive at the final slope-intercept equation: y=13x103y = \frac{1}{3}x - \frac{10}{3}.

Ensure your explanation is logical, sequential, and highlights how intermediate terms are handled.

0

1

Updated 2026-06-05

Contributors are:

Who are from:

Tags

OpenStax

Intermediate Algebra @ OpenStax

Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax

Algebra

Recall in Bloom's Taxonomy

Cognitive Psychology

Psychology

Social Science

Empirical Science

Science

OpenStax Psychology (2nd ed.) Textbook

Related