Solving Linear Equations Graphically
A linear equation is alway of the form f(x) = g(x). For example, in the equation 2x - 1 = -2x + 5 we can regard f(x) as 2x - 1 and g(x) as -2x +5.
Solving a linear equation means transforming the original equation in to a new equation that has
the function x on one side of the equal sign and a number (which is a constant function) on the other side.
In this case the 'solution equation' is x = 1.5 (why is 1.5 a function?)
The app allows you to enter a linear function f(x) = mx + b by varying m and b sliders and a function g(x) = Mx + B by varying M and B sliders.
You may solve your equation by dragging the RED, BLUE and BLACK dots on the graph in order to produce a 'solution equation' of the form x = {constant function}.
Challenge - Dragging the BLACK dot changes both functions, but
dragging the RED dot changes only the RED function and dragging the BLUE dot changes only the BLUE function.
This means that when you drag either the RED dot or the BLUE dot you are changing only one side of the equation!!
Why is this legitimate? Why are we taught that you must do the same thing to both sides of the equation?
What is true about all the legitimate things you can do to a linear equation?