# Write a system of inequalities for the following graph

There's no solution set or the solution set of the system is empty. So if you think about this line, if you think about its equation as being of the form y is equal to mx plus b in slope-intercept form, we figured out b is equal to negative 2.

So let me shade that in. The slope is 2, so it will look something like that. The purple area shows where the solutions of the two inequalities overlap. So it would be all of this stuff. If the inequality is of the form then the region below the line is shaded and the boundary line is solid. So let's first graph y is equal to 2x plus 1, and that includes this line, and then it's all the points greater than that as well. So the y-intercept right here is 1. It's going to be all of the area above it. And that's the region of the x, y coordinate plane that will satisfy all of them.

## Graphing inequalities lesson

If the inequality is of the form then the region above the line is shaded and the boundary line is solid. Graphically, we can represent a linear inequality by a half-plane, which involves a boundary line. The boundary line divides the plane into two half planes. Likewise, a solution of a system of linear inequalities is any ordered pair that is a solution for all of the inequalities in the system. The line is dashed as points on the line are not true. So let's first graph y is equal to 2x plus 1, and that includes this line, and then it's all the points greater than that as well. And just to reinforce, you could have done this anywhere. Everything You'll Have Covered Recall that a linear inequality is an inequality involving linear functions. That is the inequality that is depicted in this graph, where this is just the line, but we want all of the area above and equal to the line. So let me shade that in. If the inequality is of the form then the region below the line is shaded and the boundary line is solid. So the solution set of that first equation is all of this area up here, all of the area above the line, including the line, because it's greater than or equal to. That's the graph of y is equal to 2x plus 1.

In this case, our system is: Tutorial Details 20 Minutes Pre-requisite Concepts Students should be able to write the equation of a line from its graph and vice versa graph a line from its equationand define and graph a system of linear inequalities.

If the inequality is then a true statement, we shade the half-plane including that point; otherwise, we shade the half-plane that does not include the point.

### Writing a system of inequalities from a graph worksheet

The slope is 2, so it will look something like that. This area right here satisfies the bottom two. So there is actually no solution set. In this example, we can use the origin 0, 0 as a test point. If x is 0, y is 1, and the slope is 2. Graphically, we represent an inclusive inequality by representing the boundary line with a solid line. There's no solution set or the solution set of the system is empty. Graphs are used to show all of the values that are solutions for a system of linear inequalities. So it's all the area y is going to be greater than or equal to this line. The second inequality is y is less than 2x minus 5. It's not a dashed line. Finally, our graph should include the points x, y which satisfy the inequality We can determine these points by taking a point on one side of the line and testing its coordinates in our inequality. This line will tell us-- well, let's take this point so we get to an integer. Now, for y is greater than or equal, or if it's equal or greater than, so we have to put all the region above this. So 2x minus 5, the y-intercept is negative 5.
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