unit2

__** 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.**__

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 System 1: The relationship between the different pairs of lines is that they will intersect at a point (4,5). they have same slopes because both of the x values of each equation have the same domain. But the have a difference their range are different.

In System 2: Their is No Solution that's why the lines don't intersect ,but they have are parallel from each other because they have the same slope. The don't have the same domain.

In System 3: Same lines. Meaning that they have many solutions so they have the same slope & 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 methods for solving a finding a solution to a system of equations are by Graphing, Substitution and Elimination. **


 * __ Graphing : __ You have to find where both lines intersect. When Both equations are in linear form you can plot the y-intercept of each and use the slope and you find where both lines intersect. **


 * __ Substitution __ : you solve for one variable and the value in the other equation.You can also check if one equation is written in linear form. **

__ **Elimination**: __** You have to check if both equations are in standard form which makes it easier to solve. And **
 * eliminate a variable by making one opposite coefficients so that one variable cancels out. **


 * When you are choosing which method is best to use you have to look and check which is graphing, elimination or substitution. A technique for Elimination are when the signs are the same you multiply by a positive on the top and by a negative on the bottom. **

__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?