Not only do the points on the line satisfy this linear inequality - so does any point in the region that we have shaded. This line is the boundary that separates the plane into two halves - one containing all the solutions and one that does not. Therefore, from the above graph, both (0, 0) and (−2, 4) should solve the inequality.
Use a test point not on the boundary to determine which side of the line to shade when graphing solutions to a linear inequality. Usually the origin is the easiest point to test as long as it is not a point on the boundary.
Instructional Video: Linear Inequalities in Two Variables
Graph the solution set.
If the test point yields a true statement shade the region that contains it. If the test point yields a false statement shade the opposite side.
When graphing strict inequalities, inequalities without the equal, the points on the line will not satisfy the inequality; hence, we will use a dotted line to indicate this. Otherwise, the steps are the same.
Graph the solution set.
Given the graph determine the missing inequality.
Video Examples on YouTube:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgidGmRnYBd2wsLu3AaQyAGh9SEUrck6HExW3gxQOU5hUl3cWnkf_RVBmBcsAxz_Lk59ygL9dMscAPuz_MVYCCIzGi4Iks-MKct3itUKmcFNPbZ5fnu94cZoNKVWTqACAAJBtuu78vtj70/s1600/vid-0333.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqg0t16UdRaSHtVijcpONVviORr62RPSZntrDAer-NA3Rb6pvY9FNNR65vKGEnmDw6bgNUlM30rnyotIsQukRnYGYljymyWu3-lfi41vrpwF-m1x5O1lslR0rGvDjhHM5hCZ8CntVgMCA/s1600/vid-0334.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvStL_Euxfasxr_aKswlRyMPta5IE5ogg8EuymTr3C-kzJwN9QvvgjWefuUix77YEc6vSK8jA7YQ3-co7qXTtb8Af5s5DAnPyKCed0X0_y1Qd8MFg7082RmjF7XSvVisqgYRZOtoFmVA8/s1600/vid-0335.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPWT59UUJrMOj2MVzRs8nMKxxu0kOq7SQAZQQIUcuFKRsM-E4WGSJzDfEuZX6mk91Uo5wk6MkFuOssix4D4CwtnCVk0lVYqu-ax1_gUPgZ7R1RaT_QZPl8ZsNGOqeTAsAwdj0Y5clloIU/s1600/vid-0336.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiTSvGxn5fYDKVS5F1s63CnDZSyGKfmPZ4KHoWn1tW6Dpi2nugj54O-KAwKT3OeZmRmXLvhO_JGqQ265CEXttmYpELHulT0RS2_mPnvLd3Hc3AQP1LZlpmQrUK-FEz1wDqOtlxvo_US0Y/s1600/vid-0337.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyqFQ6P_7YBo6GRmFYy1I9y0W4L50Sq8PtbeSozwfB-rD7ChyDGONC_c380tWaQLk5rNCRbNUV2Noy0sOdoDGmxz7Rtoszx2PaGrblhKFQOcMB7PR_Tj9k_IQDef_UIUa51Enhq8xlaSk/s1600/vid-0338.png)