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Q: How are the graph of an equation and the set of all solutions of an equation related?

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The graph of an equation represents the solution set of the equation, that is all the solutions of the equation are points that lie on the graph and all the points that lie on the graph are solutions of the equation.

If it is a straight line, then the equation is linear.

It represents all solutions to the linear equation.

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When you graph the quadratic equation, you have three possibilities... 1. The graph touches x-axis once. Then that quadratic equation only has one solution and you find it by finding the x-intercept. 2. The graph touches x-axis twice. Then that quadratic equation has two solutions and you also find it by finding the x-intercept 3. The graph doesn't touch the x-axis at all. Then that quadratic equation has no solutions. If you really want to find the solutions, you'll have to go to imaginary solutions, where the solutions include negative square roots.

There are an infinite number of equations that meet that requirement. One of them is y = x

To graph the set of all the solutions to an equation in two variables, means to draw a curve on a plane, such that each solution to the equation is a point on the curve, and each point on the curve is a solution to the equation. The simplest curve is a straight line.

Graph it (the equation).

The graph of an equation is all of the answers that are true for the equation. A variable is an unknown number in an equation. Most equations are written with x and y variables. There are an unlimited amount of numbers that the variables can be to have the equation be true, so you would graph the equation to show the unlimited amount of numbers that make the equation true.

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They are all the points where the graph crosses (or touches) the x-axis.

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