# Solving Linear Equations Graphically & Symbolically

- Author:
- Judah L Schwartz

A linear equation is always 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?) This applet 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 GREEN, BLUE and WHITE dots on the graph in order to produce a***graphically**__'solution equation'__of the form**x = {constant function}**.**CHALLENGE**- Dragging the WHITE dot changes both functions, but dragging the*dot changes only the***GREEN***function and dragging the***GREEN***dot changes only the***BLUE***function.***BLUE****This means that when you drag either the**What is true about all the legitimate things you can do to a linear equation?*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 are the symbolic operations that correspond to dragging each of the dots?**You may also solve your equation*but using sliders to change the linear and constant terms on each side of the equation.***symbolically****- What are the graphical operations that correspond to each of the sliders?****What other questions could/would you ask of your students based on this applet?**