# Write a system of inequalities for each graph of a function

The content standards covered in this unit Seeing Structure in Expressions A. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group. If f is a function and x is an element of its domain, then f x denotes the output of f corresponding to the input x. Graphing two-variable linear inequalities Video transcript We're asked to determine the solution set of this system, and we actually have three inequalities right here. A good place to start is just to graph the solution sets for each of these inequalities and then see where they overlap.

And that's the region of the x, y coordinate plane that will satisfy all of them. 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. If x is 0, y is 1, and the slope is 2. If we move forward in the x-direction 1, we move up 2.

If we move forward 2, we'll move up 4, just like that. So this graph is going to look something like this. Let me graph a couple more points here just so that I make sure that I'm drawing it reasonably accurately.

So it would look something like this. That's the graph of y is equal to 2x plus 1. 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.

For any x, 2x plus 1 will be right on the line, but all the y's greater than that are also valid. 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.

So that's the first inequality right there. Now let's do the second inequality. The second inequality is y is less than 2x minus 5.

## Algebra I - Unit 4: Linear Equations, Inequalities and Systems | Common Core Lessons

So if we were to graph 2x minus 5, and something already might jump out at you that these two are parallel to each other. They have the same slope. So 2x minus 5, the y-intercept is negative 5. Slope is 2 again.

And this is only less than, strictly less than, so we're not going to actually include the line. The slope is 2, so it will look something like that. It has the exact same slope as this other line.First we graph our boundaries; we dash the line if the values on the line are not included in the boundary. If the values are included we draw a solid line as before. Second we test a point in each region. Graph inequalities In order to graph an inequality we work in 3 steps: First we graph our boundaries; we dash the line if the values on the line are not included in the boundary. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

How to Graph the Equation in Algebra Calculator. First go to the Algebra Calculator main page. Type the following: y=2x+1; Try it now: y=2x+1 Clickable Demo Try entering y=2x+1 into the text box.

After you enter the expression, Algebra Calculator will graph the equation y=2x+1. Write and graph the system of inequalities that Graph each function.

## Graph system of inequalities and find intersections step-by-step

Identify the domain and range. \$(5 D = {all real numbers}, Solve each system of inequalities by graphing. \$(5 a. Click here 👆 to get an answer to your question ️ Write a system of linear inequalities to represent each graph. 