Linear Inequalities

How to graph the equation of a linear inequality

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 inequality

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Pictured below is the graph of the line y = x

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

picture of linear inequality and its graph

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

Problem 1

What is the equation of the line on the left?

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

Problem 2

On the left is the graph of the equation y=x+1. What would the graph of y ≤ -x + 1 look like?