Unit+2+-+Linear+equations+and+inequalities

=Is **this how you feel about Linear Equations? Well, maybe we can help you study.**=


 * Topic Discussed in Class are:**
 * Graphing Linear Functions
 * Calculating a Slope
 * Writing Equations for Lines
 * Form a Graph
 * Parallel Lines
 * Perpendicular
 * Slope
 * Y-intercept

Ex: The inequality //x//-2>5 has the same solutions as the inequality //x// > 7. (The second inequality was obtained from the first one by adding 2 on both sides.) Rule 2. Switching sides and changing the orientation of the inequality sign. Parallel Lines: are used to the opposite sign reciprocal from the parallel equations. Ex: y=3x-4 Perpendicular: The Y-intercept of given lines does not matter.
 * Useful Vocabulary and Example:**
 * **Standard Form:** is a way of writing down very large or very small numbers easily.
 * Ex:** Ax+By=C A=First Rate B= Second Rate C= Total
 * **Slope**: is the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.
 * Ex:** y=mx+b **m= the slope __rise__ -(+,up)(-,down) B=y intercept.**
 * run (Always move to the right)**
 * Inequality:** is a statement about the relative size or order of two objects, or about whether they are the same or not.


 * Demand:** Refers to how much (Quantity) of a product or service is desired by buyers. The quantity demanded is the amount of a product people are willing to buy at a certian price; the relationship between price and quantity demanded is known as the demand relationship


 * Supply:** Represents how much the market can offer. The quantity supplied refers to the amount of a certain good producers are willing tho supply when receiving a certain price.

> Calculating the slope: m= __y-y__ = __rise__ > spacespacespacespaces. x-x .... run > **Ex:** (2,4) (8,-2) > __Step one:__ Look at your two points, take both Y's and put them into an equation that looks like this: 4--2 That would be correct, however when using this equation there cannot be a negative next to the subtraction sign to it gets turned into a addition sign. Therefore it would read: 4 + -2. Great, we're on the right track. > __Step two:__ Now you want to use the X's, be careful to remember what order you took the Y's you have to make sure that the X's match up with the corresponding Y's. Your equation should look like this: __4+ -2__ > spacespacespacespacespace 2 - 8__Step three:__ Now that you have your equation you should be able to solve it, first start with the top. 4 + -2 = 6. Now do the bottom half 2 - 8 = -6. Your equation will now read __6__ > . -6 Which reduces to -1 > > Ex: (m) slope = 100 (b) y- intercept = 32 > y = 100x+32
 * Additional Notes:**
 * What is a //coefficient//? The number that is multiplied by a variable, for example: 3x What is the coefficient is 3x? The 3 is the coefficient, the coefficient is usually the number that is touching the unknown variable.
 * Slope:**
 * What is slope? The measurement of the steepness of a line.
 * What does slope measure? The rate of change
 * Writing Equations for Lines:**
 * 1) Graph of a line
 * 2) The y-intercept and the slope
 * 3) A point on the line and the slope
 * 4) Two points on the line
 * 5) A point and a line that is parallel or perpendicular to the line
 * A slope and a y-intercept:**
 * Put it into the equation y=mx+b

1. One intersection- Ordered pair 2. No intersection- Parallel (Same Slope) 3. Infinite intersections- Same Line
 * System of Equations:** One or more equations that use the same variable

1. Rearrange the equation so that one of the variables is by itself. 2. Substitiute the expression for that variable into the other equation 3. Solve 4. Substitute your answer back into either of the original equations and solve for the second variable.
 * Substitution Method:**

1. Set up graph 2. Plot points 3 Connect the points
 * List of Points:**

Substitute the function in for X then Solve Ex: F(2)=4X+3X
 * Functions:**

[] In this section, you will learn how so solve inequalities. "Solving an inequality means finding all of its solutions. A "solution of an inequality is a number which when substituted for the variable makes the inequality a true statement. [] How to Find the Slope of a Line and games to teach you how to do it on your own and what you got wrong if you didn't understand a particular topic. [] Point on the graph and show you how to get the element of a graph, Identifying the x-coordinate, Identifying the y-coordinate,Notation for Identifying Points,Points On The Axes,examples and much more. [] This site will help if you missed any notes on functions or graphs. To get here click on Graphs and Functions. Also if you would like a head start on other notes you might find them in the other links posted on this web site such as Systems of Equations and Inequities. [] This is an awesome game for learning how to use slope! It also shows how slope can actually relate to your life. You will be playing basketball. Hope you brought your gym shoes! [] This website is not a game but it is a really useful page all devoted to how to write an equation of a line. After reviewing this website it showed me that it really does help you better understand how to do it!
 * Still confused? Here are some useful sites:**