Solving Linear Equations Graphically II
- Judah L Schwartz
This environment differs from the previous one in an interesting way. In this environment you enter your equation f(x) = g(x) by fitting a linear function f(x) to two blue points that you can place anywhere on the screen, and a second linear function, g(x), by fitting it to two red points that you can place anywhere on the screen. You can then, just as before, transform your original equation into the ‘solution equation’ form x = constant by dragging the RED, BLUE and BLACK dots. How do the expressions for f(x) and g(x) change as you drag the RED, BLUE and BLACK dots up and down? The same challenge applies – 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?