Just like equations, sometimes we have two variables in an inequality. Graphing inequalities with two variables involves shading a region above or below the line to indicate all the possible solutions to the inequality. When graphing inequalities with two variables, we use some of the same techniques used when graphing lines to find the border of our shaded region.
When you're graphing inequalities that have both x and y there's a three step process you want to use. First thing you want to do is graph the line using y=mx+b techniques. What I mean by that is get the y all by itself put a dot at your y intercepts from there count the slope and then connect the line. Next thing you're going to want to do is adjust the line based on if it's one of these inequalities symbols or one of these, less than and greater than ask that you draw a dotted line because those points actually are not technically solutions. You get solid line if it's one of these inequality symbols. Lastly any time you're graphing an inequality you're going to have some shading, like remember on the number line how you had to graph going out in the directions are like a dumbbell shape or whatever you had to draw some shading, the same thing is true in the xy plane only you're going to be shading like half the plane think about an xy coordinate plane with a line cutting across it, you're going to be shading either everything on one side of that line or the other side. The way to figure out which way to shade is to pick any point you want to that's not on that line substituting your x and y values to the inequality and you're going to be shading the side of the line that make the inequality true. So this is a really important three step process you might want to write down on note card or something that you can have next to you when you're doing your homework problems and if you can remember this process and keep it all straight you'll have a lot of success on these problems.
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