Use of Linear Equations

Linear equations can describe physics, business and biology. Systems of linear equations model phenomena with multiple relationships. They are a conceptual foundation for calculus-based theories of slope and are utilized in numeric approximations.

Physics

Equations of the form y = mx + b can track movement. The constant b defines the starting position, and m describes steady velocity. The variable x is the time during which movement is occurring at velocity m. Together, this information gives the total distance covered--y.

Business

In finance, if you start with $5 (b = $5) and work for 6 hours at $10/hr (m = $10/hr, x = 6 hours), after those 6 hours there is mx + b = 10(6) + 5 = $65.

Biology

Cricket chirping frequency correlates to outside temperature. A project exploring this was conducted by Jane M. Brown of the University of Illinois College of Education.

Multiple Linear Equations

Systems of linear equations can describe several object types. Scenarios involve coin types when dealing with change and amount and total mass of light/heavy weights at a gym.

Broad Mathematical Relevance

Linear equations are relevant to advanced mathematics. Newton's method is based on repeated applications of linear equations.

Intro to Calculus

Students soon understand that a steeper line has a larger (absolute) value of m. Calculus-based concepts of slope can be introduced by referring to linear equations as a beginning example.

References

• University of Illinois Urbana-Champaign, College of Education: What's in a Line?
• Lamar University: Paul's Online Notes, "Calculus 1--Newton's Method"

Resources

• Regents Exam Prep Center: Applied Practice With Systems of Linear Equations
• Interactive Mathematics: Slope of a Tangent to a Curve