Solving an Equation Graphically
The function is comprised of all the points that satisfy its function rule. If the -coordinate is already given, the result is a one-variable equation such as
where is the given -coordinate. It is then possible to use the graph of to solve the equation. For instance, the equation
can be solved using this method.
If needed, rearrange the equation
If there are variables on both sides of the equation, the equation has to be rearranged so that the variables are on the same side.
The side with the variables can now be seen as a function, Graph that function in a coordinate plane. For the equation
the function is
Identify any points with
Now, find all the points on the graph that have the -coordinate For the example, the constant has the value and there are points on the graph with the -coordinate
The -coordinates of any identified points solve the original equation, Note that solving an equation graphically does not necessarily lead to an exact answer. To verify a solution, substitute it into and evaluate the expression. If the function value equals it's an exact solution. If it's almost equal to an approximate solution has been found. In the example, the -coordinates are and
Verifying the solution is done by evaluating
We find that the function value is which is the same as the value of for this equation. Thus, it is an exact solution. The solution can be verified the same way.