Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Graphing Linear Inequalities

Use the following procedure to graph a linear inequality in two variables.

Procedure â€” To Graph a Linear Inequality in Two Variables

Step 1 Graph the equation that corresponds to the given inequality.

â€¢ If the inequality symbol is or , use a solid line to show that points on the line are solutions of the inequality.

â€¢ If the inequality symbol is < or >, use a dotted line to show that points on the line are not solutions of the inequality.

Step 2 Use a test point NOT on the line to determine the region whose points satisfy the inequality.

Step 3 Shade the region whose points satisfy the inequality.

Example 1

Graph the inequality 2x - y < 4.

Solution

Step 1 Graph the equation that corresponds to the given inequality.

Graph the equation 2x - y = 4.

To do this, substitute 0 for y and solve for x to get the x-intercept, (2, 0).

Next, substitute 0 for x and solve for y to get the y-intercept, (0, -4).

Then, plot the points.

Since the inequality symbol â€œ<â€ does not contain â€œequal to,â€ draw a dotted line through the plotted points.

The dotted line shows that points on the line are not solutions of the inequality. Step 2 Use a test point NOT on the line to determine the region whose points satisfy the inequality.

The point (0, 0) is not on the line, so it can be used as a test point.

 Substitute 0 for x and 0 for y. Simplify. IsIs 2(0) - 00 < 4 ? < 4 ? Yes

Since 0 < 4 is true, the ordered pair (0, 0) is a solution of the inequality 2x - y < 4.

This means all the points in the region containing (0, 0) are solutions.

Step 3 Shade the region whose points satisfy the inequality.

Shade the region that includes (0, 0). This is the region above the dotted line. Note â€” Using (0, 0) as a Test Point

If the point (0, 0) does not lie on the line, it is a good test point since it often makes the calculations easier.