A graphing calculator can be used to solve a linear equation of the form . The algebraic method of solving a linear equation in one variable is to multiply and add to create a final equation with the variable on one side and the answer on the other. Graphically, this is not necessary. Consider the equation . We will graph and . The x-value of the point of intersection of the two lines, x = 1.5, is our answer since we were solving for x. If we had subtracted 3x on both sides of the original equation, we would have had . Then, we would graph and . Again, the x-value of the intersection point is our answer. Note from the figures on the left that only the y-value of the point of intersection changes when you add or multiply to both sides of the equation. 

 You may have to adjust the viewing window to see the intersection point. 

Graphing Calculator Explorations

Solve the equation using the graphing method mentioned above, and show that the x-intercept of the point of intersection is your answer by using algebraic methods to solve the equation. Use the graphing method to show that {-3} is the solution to the equation . Use algebraic methods to solve . Since this is a special case for linear equations algebraically, it should also be a special case in graphing. Graph the lines.