Using a graph is just another way we can solve equations. We can solve linear, quadratic and even cubic ( see for cubic graphs).

Linear Equations Example: Say we wanted to solve 2x-1 = 3x+1, and we are given the equation y = 2x-1 on a graph.

In order to solve the equation for 2x-1 = 3x+1, we need to plot y = 3x+1 on the same graph, and see where both lines intercept one another. We then take the x co-ordinate as the solution for the equation.

So looking at the graph we can see that the lines intersect one another at x=-2

Quadratic Equation Example: Say we have the graph x2 -4x-12 given to us, and we need to solve x2 -4x-12 = x+4.

To do this, we need to plot y = x+4 on the same set of axis, then read off where y=x+4 intersects the quadratic.

We can give estimates to where the intersecting points lie on the x-axis. So one at x= -2.1 and the other at x = 7.2. Remember since this is a quadratic graph we are solving, there are two possible values can be.

To check this, we need only to put the values back into our equation x2 -4x-12 = x+4.

If x = -2.2, on one side of the equation we have (-2.2)2 - (4 x - 2.2) - 12 = 1.64. On the other hand side we have -2.2 + 4 = 1.8. 1.64 and 1.8 are quite close together so we can say that x=-2.2 is a solution.

If x=7.2, on one side of the equation we have 7.22 -4 x 7.2 - 12 = 11.04. On the other hand side we have 7.2 + 4 = 11.2. Again these two values are quite close together, so we can say that x=7.2 is a solution

As you can see, unless a line goes through a graph where x is a whole number, an estimate has to be made. You need to check that both sides are fairly similar when going to check your answers.


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