To understand how to graph the equations of linear inequalities such y ≥ x + 1, make sure that you have a good understanding of how to graph the equation of a line in slope intercept form.

A linear inequality is describes an area of the coordinate plane that has a boundary line. Every point in that region is a solution of the inequality.

In simpler speak, a linear inequality is just everything on ONE side of a line on a graph.

**Interactive** Linear Inequality

Click and drag the points on the inequality below and the graph, formula and equation will adjust accordingly. (Try clicking on equation itself to toggle between ≤,<, >and ≥ )

Try the full sized interactive linear inequalityPictured below is the graph of the line y = x

In the pictures below are the graphs of y ≥ X and Y ≤ x (respectively)

Below is the graph of the equation of the line y = x +1

Below are the graphs of y > x + 1 and y < x+1

Below is the graph of x>2 on the number line.

Below is the graph of the linear inequality X>2 on the coordinate plane

**Practice** Problem

Now, what does the graph of y > x +3 look like?