Week 11 – Math 11

This week in math 11 we learned about graphing linear inequalities in two variables. The solutions to these equations are represented by boundary lines that have shading on one of the sides, the boundary line can also be either solid or dotted/broken. You determine that by your greater than, less than, and greater than and equal to or less than and equal to symbols.

How to Graph: The first thing you can determine right away is whether the line is solid to broken. For example if you have the equation x+y<3 right away you know that this will be a broken line meaning the numbers on the line are not solutions of this equation compared to if the line was solid they would be. Next you are going to want to isolate y, you equation will now change to y<-x+3. Now you are ready to start graphing.

When you have an equation with no middle term, the second term is still the y intercept and x still gives you your slope of the line. Now you are going to move up three spaces on your y axis and then from there do your slope of \frac{-1}{1}. Remember this is a negative line.

Next you are going to want to see there the positive side of the graph is, these are all the solutions for the equation. The best coordinate to test if possible is (0,0) because is mathematically easier and you don’t have to remember to put your x and y values in the right place. For this graph (0,0) will work so once we test that its now clear to see that the left side of the line is positive and is the solution side.

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