Case Study

Logistics Fuel-Efficiency Modeling Validation

An operations supervisor at a national logistics company is developing a visual dashboard to help dispatchers monitor fleet efficiency thresholds. The system uses the mathematical inequality y<23x5y < \frac{2}{3}x - 5 to represent the safe operating zone, where xx represents the weekly mileage logged (in thousands) and yy represents the fuel efficiency index adjustment.

To ensure the automated dashboard's graphing tool is programmed correctly, the supervisor must manually document and recall the standard three-step graphing procedure for this specific linear inequality.

Your task is to write a guide for the programming team. Recall and state each of the three standard steps required to graph the inequality y<23x5y < \frac{2}{3}x - 5 on a coordinate plane. In your guide, specifically address the following for each step:

  1. Step 1 (Boundary Line): Identify the equation of the boundary line and explain whether it should be drawn as a solid or dashed line on the dashboard, explaining the rule that dictates this style.
  2. Step 2 (Test Point): Show the full substitution and simplification process using (0, 0) as the standard test point, and state whether (0, 0) is a solution to this inequality.
  3. Step 3 (Shading): Based on the result of the test point, identify which side of the boundary line (above or below) must be shaded to represent the correct safe operating zone.

0

1

Updated 2026-06-03

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