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.**__

__**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. Y intercept and slopes are different making only one solution. 2. The slopes are the same but the y intercepts are different making no solutions because the lines are parallel. 3. Because the equations are the same there is an infinite amount of solutions.

__ 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.

Combination- Usually in standard form. When I want to cancel out one variable to find the other it is combination. Substitution- When there is one variable alone on one side i would use substitution because i can easily plug in the equation into the other equation. Graphing- When both equations are in slope intercept form i prefer to graph them because it is easier. Also when i see a fraction i would graph it.

== __ 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.
 * What is the y-intercept of each function? Explain in the context of the situation.
 * What is the slope of each function? Explain in the context of the situation.
 * Which account is better? Is this always true? Be specific, using dates and account values from the graph to support your argument.
 * Which account would you choose when opening to save up for your college in a few years and why?
 * Would you choose that same account to start your child's college fund (if you had a child) and why?

 1. For the blue line the function would be y=100x+1000. For the red line the function would be y=75x+1050. 2. For the first function, or the blue line the y intercept is 1000 because it is where the line crosses the y axis. It is also the amount of money that is started with in the beginning. The red lines y intercept is 1050 because the line causes the y axis at that point. It is the amount of money started with. 3. For the blue line the slope is 100 and it is the additional amount of money that is deposited. The slope for the red line is 75 and it is also the amount of money that is deposited each time. 4. The blue one is better because after a certain point the money that is earned increases. This is not always true because before the 3rd year the red line was higher than the blue one. 5. I would choose the blue line because although i would start off with less money i would eventually be able to increase my earnings which i see as a better choice. 6. I would also want my child to choose the blue line because although they too would struggle at first they would soon have an increase in their earnings.

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