Unit+3

__ 3.1: __
** [|Graphing Simple Inequalities] **After watching the video above on graphing, you need to match the inequality statements below in the document below with their corresponding graphs.  3.1 wikispace journal.doc In your wikispace journal, explain your entire thought process (from your first match to your last) and how you narrowed down the choices and knew which graph matched which inequality statement.

Graph A would go with the algebraic expression #2 because the arrow was pointing left and it was an open circle. Graph B would go with #6 because The first line was a closed circle so it had to be <= and the other line going right was an open circle, so it would be >. Also it would be #6 because it says "OR", so that means two lines would be graphed. Graph C would go with #3 because it would have to be two circles and one line. Then I realized that it would have to be < and <= and they one is a closed circle and the other is open. Graph D would be #1 because it is pointing right and it is a closed circle and that would mean it is >=. Graph E would be with #4 because it is an "OR" and that would mean two lines being graphed. Also one is a closed and the other is an open circle. Then Graph F would be #5 because they are both closed circles and that they would only have a solution in between the two points.

== __** 3.2: **__ ==

__**Summarize what we did in class today.**__ Explain what similar features are shown in the graph x>5 as you would graph it on a number line and x>5 as you would graph it on a coordinate plane. Also explain the similarities of x<=3 as graphed on a number line and x<=3 on a coordinate plane. Explain how this same thinking applies to y<2x+1 ?? How do you know which side of the line should be shaded since the line is slanted? Be sure to explain the short-cut method as well as the algebraic method you could use to prove that the correct side of the line has been shaded.

The similar features to x>5 on a graph is that it would be shaded to the right. If x>5 was on a number line, it would also be facing right. If you graphed x<=3 it would be a solid line that would be shaded to the left. If x<=5 was on a number line it would be a closed circle and it would be facing the left side. It would apply to y<2x+1, that when you graph it on a coordinate plane that the y-intercept would be 1 and then the slope would be 2. So you would then shade it below the line since it is less than. If it was greater you would shade above the slanted line. To prove if it is correct, you would pick a point to plug in into the inequality and if it made sence then it was correct but if it wasn't, it could possibly mean than it was shaded incorrectly.

== __ 3.3: __ == __**(Looking at graph on page 113)**__ Write the inequality whose graph is shown. Explain every step of your thinking and how you came up with the inequality.

y<=-1/2x+4 I first looked at the y-intecerpt (4). . It was a solid line and that meant that it was either <= or >=. It was shaded below so then it had to be <=. Then I looked for the slope and determined if it was a negative or postive. The slope was -1/2. So then I put all of that together to get y<=-1/2x+4.

== __ **3.4:** __ == Looking at the shaded graph in the document below, you need to identify a point that is a solution to the system and explain how you know it is a solution by looking at the graph. Also, identify a point that is a solution to only one of the inequalities, but NOT a solution to the system. Explain how you might test a point to determine whether it is a solution to the system or not?

A solution to the graph would be (-8, 4). It would be a solution because it is in the double shaded area, which means that it would be a solution for both of the inequalities. A point that would not be a solution would be (-8, 1). It would not be a solution because it is on the dotted line. That means that it is not a solution because it wouldn't include the number on the dotted line, but it would if it was on the solid line.