Understanding the Graph of Linear Inequality 6x + 2y ≤ 10

What is a Linear Inequality?

A linear inequality is an equation that has a greater than, less than, or equal to sign instead of an equal sign. It is used to describe a region of the x-y plane. This particular type of equation can be represented as a graph, which can be used to show the boundaries of the region.

How to Graph a Linear Inequality

Graphing a linear inequality is fairly simple, and requires only a few steps. First, note the sign of the inequality. If it is less than or equal to, the boundary line will be solid. If it is greater than or equal to, the boundary will be dashed. Next, plot the points on the x-y plane. Then, draw the boundary line between the points. Finally, shade in the appropriate region.

An Example: Graph of Linear Inequality 6x + 2y ≤ 10

Let’s take a look at a specific example. The graph of linear inequality 6x + 2y ≤ 10 can easily be graphed using the steps above. First, note that the inequality is less than or equal to, so the boundary line will be solid. Then, plot the points that are solutions to the equation, which in this case are (2,2) and (1,4). Draw the line between these points, and then shade in the region that satisfies the inequality.

Conclusion

Graphing linear inequalities is a useful tool for understanding the boundaries of a region. With the steps above, you can easily graph the graph of linear inequality 6x + 2y ≤ 10. All you need to do is plot the points, draw the line, and shade in the region that satisfies the inequality.