Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*
The purpose of this lesson is for students to understand how to analyze a system of equations to determine when a plan is cheaper, more expensive, or cost the same at certain points on the graph.
It’s amazing to get to the point where students truly understand how useful and beautiful algebra can be. Transitioning from graphing systems to solving by substitution is an opportunity to get kids there.
A little over a week into a systems unit, it's important to take a little time to meet kids where they are and assess where they're at. Today's work will serve as a springboard to the next few days.