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 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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Examine the 3 graphs below to understand how linear inqualities relate to a linear equation.

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
Examine the 3 graphs below to understand how linear inqualities relate to a linear equation.

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

The equation of $$ y ≥ x +1 $$

The equation of $$ y ≤ x +1 $$

The graph of $$ y > x + 1 $$

The Graph of $$ y < x+1$$

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

On the right, is the graph of the equation $$ y=x+3 $$. What would the graph of $$ y > x + 3 $$ look like?

Problem 2

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


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