# Solving Linear Equations Graphically & Symbolically

- Author:
- Judah L Schwartz

- Topic:
- 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 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__**graphically***,***GREEN***and***BLUE***dots on the graph in order to produce a 'solution equation' of the form x = {constant function}.***WHITE***- Dragging the***Challenge***dot changes both functions, but dragging the***WHITE***dot changes only the***GREEN***function and dragging the***GREEN***dot changes only the***BLUE***function. This means that when you drag either the***BLUE***dot or the***GREEN***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***BLUE**__by 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 the sliders.__**symbolically**