unit+2+journal

__**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.

In the first graph there is one solution the slopes and the y-intercept are different 2. there is no solution because the slopes are the same and the y-intercepts are different. The third graph has infinite solutions because the equations are exactly the same and 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.

The 3 different methods for solving equations are graphing, combination, and substitution. When I have an I would use the method of graphing. When I have a variable by itself I want to to get rid of it and so I have can the other one to solve I would use combination. When the x is on one side of one equation and on the other equation when the y is on one side the you would substitute one of the variables to solve it. With each method I am trying to find the solution of both equations. So when I get the solution I can graph it.

<span style="color: #000000; font-family: 'Comic Sans MS',cursive;">**__2.3__** <span style="color: #000000; font-family: 'Comic Sans MS',cursive;">Look at the graph below. Both functions represent two different bank accounts.

<span style="color: #000000; font-family: 'Comic Sans MS',cursive;">**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.**

<span style="color: #000000; font-family: 'Comic Sans MS',cursive;">**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.**

<span style="color: #000000; font-family: 'Comic Sans MS',cursive;">Compare and contrast the two bank accounts in your online journal by answering the following questions:
 * <span style="color: #000000; font-family: 'Comic Sans MS',cursive;">Write a function that represents the red linear function.
 * <span style="color: #000000; font-family: 'Comic Sans MS',cursive;">What is the y-intercept of each function? Explain in the context of the situation.
 * <span style="color: #000000; font-family: 'Comic Sans MS',cursive;">What is the slope of each function? Explain in the context of the situation.
 * <span style="color: #000000; font-family: 'Comic Sans MS',cursive;">Which account is better? Is this always true? Be specific, using dates and account values from the graph to support your argument.
 * <span style="color: #000000; font-family: 'Comic Sans MS',cursive;">Which account would you choose when opening to save up for your college in a few years and why?
 * <span style="color: #000000; font-family: 'Comic Sans MS',cursive;">Would you choose that same account to start your child's college fund (if you had a child) and why?




 * <span style="color: #000000; font-family: 'Comic Sans MS',cursive;">y=100x+1000 is the function for the blue line & y=75x+1050 is the function for the red line.
 * <span style="color: #000000; font-family: 'Comic Sans MS',cursive;"> the blue, the y-intercept is 1000 because that's how much money you started with and that's where intersects with the y axis. In the red line the y-intercept is 1050 because that's how much money is started with this equation and where it intersects with the y axis.
 * <span style="color: #000000; font-family: 'Comic Sans MS',cursive;">100x is the slope of the blue line because that is what's making the line increase or decrees. 75x is the slope of the red line because that is what's making the line constant by going up or down.
 * <span style="color: #000000; font-family: 'Comic Sans MS',cursive;">The blue line account is better because after the 3rd year more money is earned rather than the red line which would be less than the blue line,
 * <span style="color: #000000; font-family: 'Comic Sans MS',cursive;">If I opened an account for college fund in a few years I would pick the red line because I would start off with more money in the first few years
 * <span style="color: #000000; font-family: 'Comic Sans MS',cursive;">If I opened an account for my child's college fund I would pick the blue line because my child would have more money later on.