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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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Use it to enable or disable snapping

Click on the equation to change inequality type between ≤, <, > and ≥

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.

y = x

The graph of $$ y ≤ x $$.

linear inequality: y >= x

The graph of $$ y ≥ x $$.

linear inequality: 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 $$ y = x + 1 $$.

linear inequality: y = x + 1

The equation of $$ y ≥ x + 1 $$.

linear inequality: y >= x + 1

The equation of $$ y ≤ x + 1 $$.

linear inequality: y <= x + 1

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

Linear inequality: y > x + 1

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

Linear inequality: y < x + 1

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

Linear inequality: x > 2

Below is the graph of the linear inequality $$ x >2 $$ on the coordinate plane.

Linear Inequality: x > 2