# Week 11 – PreCalculus 11

This week in PreCalculus 11 we were introduced to our new unit of Graphing Linear Inequalities and systems.

Linear inequalities will give us a straight line on a graph. When we are given inequalities we are usually given a y value that is greater than or equal to another value, that consists of an x variable. We can also be given a greater than/less than or equal to symbol. This greater than or less than help us decide which side of the line contains the real answers, which we shade in. We also need to determine if the line is broken or solid. The way we can determine that it is greater/less than (>,<) then it is a broken line. If it is greater/less than or equal to $(>=,<=)$.

If we are given the equation of 3x + 7 < y. Just from looking at this equation we can determine the y-intercept which is 7. We can also determine the slope which is 3/1, which means it goes up 3 and over 1 each time.

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To know whether or not which side of the line contains the real answer, we must perform a test. We will insert the point (0,0) into the equation if it comes out there (left side equals to the right side). If we insert 0 then we will get that 7<0 which is false so we would shade in the right side of the line.

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The last and final thing that I need to mention is that you need to remember that one must remember to switch the signs if the coefficient of x is negative.