Graphing Linear Inequalities

Steps to GraphingA two-variable linear inequality

When you graph an inequality, start as you would with any equation.

Steps to GraphingA two-variable linear inequality

Determine the region for the solution.

(“ means y is going tobe below or on the line,so the boundary line issolid and the regionbelow is shaded.)

Steps to GraphingA two-variable linear inequality

Shade the solution area.

(“ means y is going tobe below or on the line,so the boundary line issolid and the regionbelow is shaded.)

Steps to GraphingA two-variable linear inequality

When “y” is isolated:

o“<” dotted line, shade below

o“>” dotted line, shade above

o“≤” solid line, shade below

o“≥” solid line, shade above

** This only works when the y-variable is isolated as in slope-intercept form. This does not work on other forms.

You try one:

Why is it helpful to have the variable y alone on the left side of the inequality?

It’s easy to read/graph: <, ≤ shade below; >, ≥ shade above.

Graphing inequalities in Standard form:

(0,4)

(6,0)

Determine the intercepts of the equation and plot them

Standard form:

(0, 0)

Pick a test point: 2(0) + 3(0) < 12? True or false?

True! So shade the region containing the test point.

Draw the appropriate boundary line, either solid or shaded.

Standard form:

When is standard form convenient for graphing?

When the intercepts are integer values.

You try one:

You try one:

You try one:-2

Food for thought

oWhat happens if you test a point on the boundary?

oWhat does the dashed boundary line on the graph of an inequality represent?