# Solving Linear Equations Graphically & Symbolically

- Author:
- Judah L Schwartz

- Topic:
- Algebra, Equations, Linear Equations

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 values for m and b in the linear function f(x) = mx + b and values M and B in the linear function g(x) = Mx + B.
You may solve your equation graphically by dragging the GREEN, BLUE and WHITE dots on the graph in order to produce a 'solution equation'
of the form x = {constant function}.
Challenge - Dragging the WHITE dot changes both functions, but
dragging the GREEN dot changes only the GREEN function and dragging the BLUE dot changes only the BLUE function.
This means that when you drag either the GREEN 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?
What are the symbolic operations that correspond to dragging each of the dots?
You may also solve your equation symbolically but using sliders to change the linear and constant terms on each side of the equation. What are the graphical operations that correspond to each of these sliders?

**What questions could / would you ask your students based on this applet?**