Instead of graphing the usual y = mx + b, which you’re still going to need to do, in these inequalities you are also going to have to shade all of the regions for which it is correct.  These are functions of the form

y ≥ mx + b    or y ≤ mx + b

Do keep in mind that they could be just > or < as well.  When doing these you begin by graphing the function the same way you would any linear function.  Find the y-intercept, and use the slope as a rise over run to make a few dots and connect the line.  The only difference is the shading.  Although there are two ways to solve the shading, one which we will use later a lot more, and one which is fairly easy.  If it is ≥ than, then you will literally draw the line and then move your pencil up, and shade the region ABOVE the line.  If it’s ≤ you will draw the function and then take your pencil and go straight down from the line and shade the region.

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This method might be a little sleazy, and the correct way is to actually test a point such as (0,0) by filling it into the inequality.  If it works out to be TRUE, shade the side that has (0,0).  If it works out to be FALSE shade the side that does NOT have (0,0)

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If you would like some practice in graphing a single inequality, try the activity below.  It will allow you to try sketching an inequality and then check your answer.  Don’t worry if you aren’t exactly correct, the purpose of this activity is to double check to see if you are on the correct path.

The video below works through an example where we aren’t given the function as a nice y=mx+b and instead have to use intercept form.  It would be a good idea to take a look at that method of graphing as it shows up fairly frequently when working with inequalities.