How are graphs and equations related?

Answer 1

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.

Answer 2

They are not.

Some graphs are based on equations but not all of them.

Conversely, while many equations that you would come across in basic mathematics can be graphed, there are many more (in advanced mathematics) that cannot be graphed.

If you want an example of the latter, consider the following function:

f(x) = 1 when x is rational

f(x) = 0 when x is irrational

Try graphing that for 0<x<1 (or any interval of your choosing).

Answer 3

Graphs help you solve equations, and equations help you solve graphs.

Because the graph is a diagram of the equation, showing at its simplest the y answer for each value of x.