A linear equation is always of the form [b]f(x) = g(x)[/b]. [br]For example, in the equation [b]2x - 1 = -2x + 5[/b] we can regard f(x) as 2x - 1 and g(x) as -2x +5.[br][br]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. [br]In this case the [u]'solution equation'[/u] is [b]x = 1.5[/b] (why is 1.5 a function?)[br][br]This applet allows you to enter a linear function [b]f(x) = mx + b[/b] by varying m and b sliders and a function [b]g(x) = Mx + B[/b] by varying M and B sliders.[br][br]You may solve your equation [size=100][size=150][i][b]graphically[/b][/i][/size][/size] by dragging the GREEN, BLUE and WHITE dots on the graph in order to produce a [u]'solution equation'[/u] of the form [b]x = {constant function}[/b].[br][br][b]CHALLENGE[/b] - Dragging the WHITE dot changes both functions, but dragging the [color=#00ff00][i][b]GREEN[/b][/i][/color] dot changes only the [color=#00ff00][i][b]GREEN[/b][/i][/color] function and dragging the [color=#1e84cc][i][b]BLUE[/b][/i][/color] dot changes only the [color=#1e84cc][i][b]BLUE[/b][/i][/color] function.[br][br][b]This means that when you drag either the [color=#00ff00][i]GREEN[/i][/color] dot or the [color=#1e84cc][i]BLUE[/i][/color] dot you are changing only one side of the equation!! Why is this legitimate? [br][br]Why are we taught that you must do the same thing to both sides of the equation?[/b][br][br]What is true about all the legitimate things you can do to a linear equation? [b][br]- What are the symbolic operations that correspond to dragging each of the dots?[/b][br][br]You may also solve your equation [size=150][i][b]symbolically[/b][/i][/size] but using sliders to change the linear and constant terms on each side of the equation. [b][br]- What are the graphical operations that correspond to each of the sliders?[br][br][/b][color=#ff0000][b]What other questions could/would you ask of your students based on this applet?[/b][/color]