Let's start from the basic concepts.
An equation in one variable is a question of what number or numbers make a statement true. For example, x + 2 = 5 has one single solution. The only number that makes that statement of equation true is x = 3 because 3 + 2 = 5, 5 = 5. An equation in one variable can have more than one solution, for example, if you have a quadratic equation such as x^2 = 9, where both x = -3 and x = 3 are solutions. But let's limit this discussion to linear equation and inequalitites (inequations).
An equation of the form ax + by = c, where a, b, and c are real numbers is a linear equation. For a fixed a, b, and c, for example, if you consider the equation
2x + y = 6, has an infinite number of solutions. Any ordered pair (x, y) whose values make the equation true is a solution. For example, (1, 4) is a solution becasue 2(1) + 4 = 6, 2 + 4 = 6, 6 = 6 which is a true statement. There is an infinite number of other ordered pairs that satisfy the equation and are solutions to it. For example, (2, 2), (0, 6), and (3, 0) are other solutions to that equation. If all the solutions are plotted on an x-y coordinate plane, all the solutions are points on a line, hence the name "linear" which comes from "line."
Now let's look at an inequality in one variable. here instead of looking for a single value of a variable that makes a statement true, you are looking for many values that make a statement true. If you have the inequality x > 8, then all numbers greater than 8 satisfy the inequality. The solution is not a single number, but a whole set of numbers that can be shown on a number line.
The next step is a linear ineqaulity. For example, x + y > 5. You are looking for all points (x, y) that make that statement true. (5, 5), (1, 6), and (6, 2) are examples of points that satisfy that inequality. (2, 3) is an example of a point that does not satisfy it becasue 2 + 3 is not greater than 5. The graph of a linear inequality is a half-plane. In order to plot it, you plot the corresponding equation to the inequality. The corresponding equation is obtained by simply repacing the inequality sign by the equal sign. First, the corresponding equation is plotted. Since it is a linear equation, its plot is a straight line. It is plotted using a solid line if the inequality sign is >= or <=, and with a dashed line if the inequality sign is simply > or <. Then you must choose a point on one of the half-planes that the line divides the entire plane into. If that point satisfies the original inequality, the entire half-plane that point lies in also satisfies the inequality, and you shade that half-plane. If the point does not satisfy the original inequality, then you shade the other half-plane.