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How to Solve Equations by Graphing

Now you’ll learn to solve equations by graphing. I’ll explain what to look for and how to read off the solution.

You can think of an equation as two functions connected by an equal sign. That means you can draw the graph for the left expression and the right expression by putting “ $y =$ ” in front of each of them.

Example 1

Solve the equation $2 x + 4 = 0$ by graphing.

1.: Graph the left side of the expression in a coordinate system, $y = 2 x + 4$ .
2.: Graph the right side of the expression in a coordinate system, $y = 0$ .
3.: Mark the point where the graphs intersect. It will look like this:
4.: Read off the $x$ -value of the intersection. From the figure you can see that the graphs intersect in $x = - 2$ .

Rule

Graphic Solution of an Equation

1.: Graph the left side of the equation in a coordinate system.
2.: Graph the right side of the equation in the same coordinate system.
3.: Mark the points where the graphs intersect.
4.: Read off the value of $x$ at the intersection.

Example 2

Solve the equation $x^{2} = 4$ by graphing.

1.: Graph the left side of the expression in a coordinate system, $y = x^{2}$ .
2.: Graph the right side of the expression in the coordinate system, $y = 4$ .
3.: Mark the points where the graphs intersect. Your coordinate system will now look like this:
4.: Read off the $x$ -values at the intersections. You can see in the figure that the graphs intersect at $x_{1} = - 2$ and $x_{2} = 2$ . That means the solution is $x = \pm 2$ .

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