Using Linear Graphs to Solve Real-World Problems

Miacademy & MiaPrep Learning Channel

This instructional math video bridges the gap between theoretical graphing concepts and real-world problem solving. It demonstrates how to interpret key features of linear graphs—specifically slope, x-intercepts, and y-intercepts—to answer practical questions about distance, profit, and physical measurements. The video uses three distinct scenarios to illustrate these concepts: a hiker walking home, an ice cream vendor seeking a profit, and a river's water level decreasing over time. The video focuses on three primary mathematical themes: (1) Understanding slope as a unit rate and using it for unit conversion (dimensional analysis), (2) Identifying the x-intercept as a "break-even point" where a value reaches zero, and (3) Recognizing the y-intercept as an initial value or starting condition (when x=0). It emphasizes distinguishing between mathematical values (like a negative slope) and their physical interpretations (speed is positive). For educators, this video is an excellent resource for Applied Algebra or Pre-Algebra classes. It moves beyond rote calculation to conceptual understanding, helping students see *why* we calculate slope or intercepts. The visual overlays showing dimensional analysis provide a strong cross-curricular link to science, while the business application offers a practical financial literacy moment. It effectively models how to extract hidden information from a visual representation.