How to Solve Equations Graphically

Miacademy & MiaPrep Learning Channel

This video tutorial provides a clear, step-by-step guide on how to solve algebraic equations using graphical methods. The instructor, Toby, demonstrates the fundamental concept that the solution to an equation f(x) = g(x) can be found by graphing the two separate functions y = f(x) and y = g(x) and identifying the x-coordinate of their intersection point. The video covers linear equations that can be solved by hand, as well as more complex non-linear equations requiring estimation or graphing technology. Key themes include the connection between algebraic equality and graphical intersection, the use of graphing calculators (or online tools like Desmos and GeoGebra) to approximate irrational solutions, and interpreting visual data to determine the number of solutions a system possesses. The lesson progresses from exact integer solutions to estimation techniques and finally to analyzing solution counts based purely on visual graphs. For educators, this video serves as an excellent bridge between algebraic manipulation and visual understanding. It validates the use of technology in mathematics and provides a strategy for solving equations that may be difficult or impossible to solve analytically at a high school level. The content is directly applicable to Algebra 1 and Algebra 2 curricula, specifically focusing on systems of equations and function analysis.