UNIT+2

__** 2.1: **__
Using a sheet of graph paper, graph each pair of equations on the same coordinate system. (There should be 2 lines on each graph.) __**You may use the document link below to help organize your thinking process and for the coordinate planes.**__

[|2.1 journal response.doc]

Answer the following questions __**on your graph paper or on the document you printed**__ and put your work in your classroom binder.
 * Identify how many intersections are shown on each graph.
 * Now look at the 2 equations that made the first graph. What is the relationship of their slopes?
 * Looking at the 2 equations that made the second graph, what is the relationship between their slopes?
 * Looking at the 2 equations that made the third graph, what is the relationship between their slopes?

__**On your wikispace**__, describe the relationship between different pairs of lines and their slopes as it relates to the number of intersections (solutions) that the system of equations will have. Be sure to discuss all 3 graphs and how they are similar or different. 1. In this there is one solution when there is one solution, thhe x and y int are both dif. 2. In this graph there is no solution because the is the same and the y-intercept is different which says that there are no solutions. 3. This graph has infinite or (never stops) solutions because the equations are the same and they have the same slope and y-intercept.

__ 2.2: __
Describe the 3 different methods for solving (finding a solution) to a system of equations. Why/When would you choose one method over the another? What are you looking for in each system to determine the best method? Discuss any tricks or special techniques to remember when solving each of the methods.

elimination, graphing, and substitution. elimination both equations are in standard form. You use the distributing property to take the variable, then solve for the other one. Then you put in the variable you solved for in, and solve for the second one. when you check your answer, put in your answers into the equations. Graphing is used when there are two equations and you're trying to find a solution by looking at it. The equations have to be in mx+b form. Substitution is used when ONLY one of the equations are in slope-intercept form. Put in that equation in to the other equation where the variable is and substitute for the variable. Then, distribute and solve for a variable. To find the other variable, plug in your solution to the equations and solve. My favorite method is elimination graphing because i find it way easyer. scence i dont like to do some math graphing is easyer.

__ 2.3: __Look at the graph below. Both functions represent two different bank accounts.


 * The blue linear function represents a bank account where a person deposited $1000. This person then deposits an additional 100 dollars at the end of each year.**


 * The red linear function represents a bank account where a person deposited $1050. This person then deposits an additional 75 dollars at the end of each year.**

Compare and contrast the two bank accounts in your online journal by answering the following questions:


 * Write a function that represents the red linear function.
 * f(x)=2x+1
 * What is the y-intercept of each function? Explain in the context of the situation.
 * y int 1150
 * What is the slope of each function? Explain in the context of the situation.
 * up 3 over to the right 2
 * Which account is better? Is this always true? Be specific, using dates and account values from the graph to support your argument.
 * red line, not really. the red line starts off bad but then as it goes on it gradually gets better rather than getting worse
 * Which account would you choose when opening to save up for your college in a few years and why?
 * red line, its way cheaper
 * Would you choose that same account to start your child's college fund (if you had a child) and why?
 * yes, because its cheaper.