UNIT+3

__ 3.1: __ A 2 B 3 C 6 D 1 E 4 F 5
 * [|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.

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

When you graph the equation on both a coordinate plane and a number line both show the solutions to the equation. when you graph on a coordinate plane you shade either above or below the line to symbolize (<: below line >: above line) the solutions. on a number line you shade in the direction of the arrow. Also when the sign is the line on the graph would be solid but if its or equal to and the circle on the number line would be closed but if its the line on the graph would be dotted and the circle on the number line would be open. Given the equation y<2x+1 the line on a coordinate plane the line would be dotted and the y-intercept would be 1 and the solutions would be below the line. the shortcut is finding the slope first then the y intercept and weather the line is going to be shaded or dotted.

__ 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}. Then I looked at the line and how it is shadded. It was a solid line and that indicates 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 slope. The slope was -1/2, so i pluged it all in 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). Its a solution because it is in the double shaded area, which means that it would be a soultion for both of the inequalities. A graghic point that would not be a solution is (-8,1), It would not be a soution because it is on the the dotted line. That means that it is not a solution because it is not on the dotted line, but it would if it was a solid line. A way to see if a graghic point was a solution is by plugging it in into the inequality and making sure the solution all makes scence.