The below diagrams will give you a clear idea where you plot graph for different signs

A dotted line is used to show when an inequality is as it states; either less than or greater than.

A solid line is used to show when an inequality less than or greater than, while being equal to. In an inequality, it also includes the number stated in the inequality depending on what direction the arrow is in.

A dotted line is for when an inequality is not equal to. It should look like < or this >. A solid line is when an inequality is equal too. It'll have the line underneath __<>__.

If it has the equal sign underneath, it's a solid line. If it doesn't, it's a dotted line.

Hello, please take a look at the following discussion to understand when to draw a solid line and when to draw a dotted line.

A solid line means the line is part of the solution and dotted line means that the line is not part of the solution.

Let's take an example, y \geq x + 3 . We want to graph all points (x, y) such that the x and y coordinates satisfy the condition y \geq x + 3 . Obviously, all points on the line y = x + 3 satisfy the condition that y \geq x + 3 . Therefore, when we shade the sky that all points above this line satisfy the condition, we draw a solid line to show that all points on the line along with the shaded portion above the line are part of the solution.

However, when y \gt x + 3 , we shade the sky, but draw the line to be dotted to indicate that while all points above the line are part of the solution, the points that lie on the line themselves are not part of the solution.