# Graphing Linear Inequalities

A** linear inequality** in two variables has the
following possible

forms:

Where a, b, c ∈R and (a, b) ≠ (0,0)

Ex.

Graph the inequality:

x + 3y ≥ 6 .

Note: The points on the line x+3y=6 will be a part of the solution

set of the above inequality.

Step 1: Find the x and y intercepts of x+3y=6. ( Two
points

determine a line).

Step 2: Since the inequality is of the form ≥ , we will draw a solid

line passing through the intercepts, otherwise we will draw a

dashed line.

Step 3: The points lying on the line in step 2 are part of the

solution set but there are others as well. In fact, the line separates

the plane in two half-planes: The upper plane and lower planes.

The plane containing the points satisfying the inequality will give

the solution to the inequality.

**To find the solution: We choose a point (We will call this the
test point) not on the boundary and evaluate the inequality at
those values. If the statement is True, then the solution set is
that region. If the statement is False, the solution set is the
other region.**

Step 4: Shade the appropriate region.

Note: The point (0,0) is a good test point to use as long as it is not

on the boundary.

Another way to identify the region satisfying the inequality is to

solve the inequality for y. Remember the various rules for

inequalities.

a) When multiplying or dividing through an inequality

by a negative number, we must change the direction

of the inequality.

b) When taking reciprocals on both sides, we must

change the direction of the inequality.