# 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 already 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
Y X
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#### You can drag the points to change the line equation

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.

The graph of $$y ≤ x$$.

The graph of $$y ≥ x$$.

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.