Sketch the graph of each linear inequality calculator

Instructions: Enter an Inequality below (Ex: y > 1-2x) and press the Arrow Right button.

Step1: Enter the Inequality as shown below and its graph shows immediately to the right.

Note: To graph multiple regions (this occurs when compound or multiple inequalities are given such as x>1 and x<3) just enter additional inequalities. Again, Graphs of GREATER THAN and LESS THAN inequalities can be graphed simultaneously.

Step1: Enter the Equation as shown below and its graph shows immediately to the right.

Note: To graph multiple equations just enter them below the first equation.

Step1: Press Y= to enter the Equation Editor. Move the cursor to the left of Y1 and press ENTER until you see the upper triangle (to graph GREATER THAN inequality) as shown in image below. And enter the Inequality to the right of Y= .

Step2: Press the GRAPH button on the top right to graph the Inequality. That's it. You now see the inequality graph as shown below.

Note1: To sketch LESS THAN inequalities you have to select the lower triangle to the left of Y=. Then the region below the function will be shaded.

Note2: To graph multiple regions (this occurs when compound or multiple inequalities are given such as y>2 and y<5) use Y2, Y3 to enter additional inequalities. Graphs of GREATER THAN and LESS THAN inequalities can be graphed simultaneously.

Step1: Press Y= to enter the Equation Editor and enter the Equation to the right of Y= .

Step2: Press the GRAPH button on the top right to graph the Equation. You now see the graph of the Equation as shown below.

Note1: To graph multiple equations enter those as Y2, Y3, etc.

Note2: To distinguish the 2 graphs I made the 2. graph thick. Notice the thick line selection left of Y2.

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VOCABULARY

Linear inequality in two variables The result of replacing the 5 sign in a linear equation with <,≤,> or ≥

Solution of an inequality in two variables An ordered pair (x, y) that produces a true statement when the values are substituted into an inequality in two variables x and y

Graph of an inequality in two variables The set of points that represent all solutions of the inequality

Half-plane Either half of the coordinate plane that is divided by the boundary line of a linear inequality

Example 1 Check solutions of a linear inequality

Tell whether the ordered pair is a solution of 3x - 4y > 9.
a. (2, 0) b. (2, 21)

Solution
a.
3x - 4y > 9 Write inequality. 3(

b.
3x - 4y > 9 Write inequality. 3( 2 ) - 4( -1 )

GRAPHING A LINEAR INEQUALITY IN TWO VARIABLES

Step 1 Graph the boundary line. Use a dashed line for < or >, and use a solid line for ≤or ≥.
Step 2 Test a point not on the boundary line by checking whether the ordered pair is a solution of the inequality.
Step 3 Shade the half-plane containing the point if the ordered pair is a solution of the inequality. Shade the other half-plane if the ordered pair is not a solution.

Example 2 Graph a linear inequality in two variables

Graph the inequality

Step 3 Shade the half-plane that

Example 3 Graph a linear inequality in one variable

Graph the inequality x ≥ 4.

Solution

Step 1 Graph the equation x 5 4. The inequality is ≥, so use a solid line.

Step 2 Test (0, 3) in x ≥ 4. You only substitute the x-coordinate because the inequality does not have the variable y . 0 ≥ 4 x

Step 3 Shade the half-plane that does not contain (0, 3), because (0, 3) is not a solution of the inequality.

Guided Practice Graph the inequality.

1. 2y + 4x > 8

2. y < 2

How do you sketch the graph of a linear inequality?