Graphing Inequality : lx-yl + lxl - lyl ≤ 2

In summary, the conversation discusses the request for a clear answer and careful graph to sketch the region in the plane consisting of points (x,y) that satisfy the given inequality. The user is also reminded to show their work when asking for help.
  • #1
Kyle1
4
0
Sketch the region in the plane consisting of all points (x,y) such that lx-yl + lxl - lyl ≤ 2
I don't know exactly the most appreciated solution to this kind of problem. Can you guys show me a clear answer and if possible, a careful graph please?
 
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  • #2
Hello and welcome to MHB, Kyle! :D

We ask that our users show what they have tried when posting questions, as this let's our helpers know where you are stuck or what you may be doing wrong, and this way we can offer you the best help possible.

Can you post your work so far?
 

FAQ: Graphing Inequality : lx-yl + lxl - lyl ≤ 2

What is the purpose of graphing an inequality?

Graphing an inequality allows us to visually represent a range of values that satisfy the inequality. It helps us understand the relationship between the variables involved and identify the solutions to the inequality.

How do I graph an inequality?

To graph an inequality, you need to first rearrange it in slope-intercept form, y = mx + b. Then, plot the y-intercept at b and use the slope, m, to find other points on the line. Finally, shade the region above or below the line, depending on the inequality symbol.

What do the different regions on the graph represent?

The regions on the graph represent the solutions to the inequality. For example, if the graph is shaded above the line, it means all the points in that region satisfy the inequality. If the graph is shaded below the line, it means none of the points in that region satisfy the inequality.

How do I determine if a point is a solution to the inequality?

To determine if a point is a solution to the inequality, you can plug in the x and y values of the point into the inequality. If the inequality is true, then the point is a solution. If the inequality is false, then the point is not a solution.

Can I use a calculator to graph an inequality?

Yes, many graphing calculators have the capability to graph inequalities. You can enter the inequality in the calculator and it will plot the graph for you. This can be helpful for more complex inequalities with multiple variables.

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