When dealing with an equation containing two variables, we can put the graph of the equation on the coordinate plane because the number of variables is equal to the number of dimensions that are needed to properly graph the solution. Each axis on a graph represents one variable in the equation being graphed. What would you use to graph the solution to an equation with one variable? What would you use to graph the solution to an equation with three variables? Could you graph an equation containing more than four variables? Explain.

If you were given the graph of an equation with two variables on a coordinate plane, what would happen to the graph if all the y-values were increased by 1? What would happen to the graph if all the x-values were increased by 1? What would happen to the graph if all the y-values were multiplied by 2 or by 1/2? Explain.

A linear equation with two variables may appear in the form of Ax + By = C, and the resulting graph is always a straight line. The equation is more often in the form of y = mx+b, where m is the slope of the line of the corresponding figure and b is its Y-axis intercept, that is, the point where the line meets the Y-axis.

For example, 4x + 2y = 8 is a linear equation because it fits the desired structure. But for graphical and most other purposes, we often write this as y = - 2x + 4.

In this unit, on the basis of this linear equation, the equal sign is changed to the greater than a sign or less than sign, which is a new challenge in the operation of symbols.