Explain The Graph of an Equation and The Graph of an Inequality ?

Here is the graph of the equation y = x. Notice that for every point along the line shown in the graph, the y-coordinate is equal to the x-coordinate. Any point whose y-coordinate is not equal to its x-coordinate does not lie on the line.

Example: the graph of the inequality

Here is the graph of the inequality x>-1. All the points whose x-coordinates is greater than -1 are included the shaded area.
The shaded area is supposed to extend indefinitely to the right, up and down. Obviously, we can't actually show that picture. But we can indicate it by not drawing any boundaries along those edges of the shaded area.

The edge which does get shown is dotted, to indicate the edge itself is not part of the graph.

You're probably asking: "How did you know where to draw the edge? " Well, think for a moment... you want to graph all the points whose x-coordinate is greater than -1. Some points have x-coordinates greater than -1, some less than, and some equal to. Which points are located on the boundary?

Those with x-coordinates equal to -1. So, the edge of this graph is the line x = -1.