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
System 1: Since this system had niether the same y-intercept or slope there is only one solution it will have which is, in this case, (4,5).
System 2: This system has equations that has the same slope resulting in parallel lines. Therefore, there is no solution.
System 3: This system of equations contains the same slope and y-intercept making it the same line. It has infinite 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.
Elimination:
Substitution:
Graphing:Used when we are given a set of equations where it is in slope-intercept form
Special Trick: CHECK ANSWERS.. plug in the variables to an equation.
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)= 75x + 1050
What is the y-intercept of each function? Explain in the context of the situation. : Y-intercept of each function means the amount of money that a person deposit to their account.
What is the slope of each function? Explain in the context of the situation.: The slope of the blue function 100x and 75x for the red. The slope of the function is the additional amount of money added at the end of each year
Which account is better? Is this always true? Be specific, using dates and account values from the graph to support your argument.
After the first year the blue account was better because it saved more money, faster. However, the red account did start out with a little more money than the blue account.
Which account would you choose when opening to save up for your college in a few years and why?
I would choose the blue account because I would want to make sure we would have enough money saved up as possible.
Would you choose that same account to start your child's college fund (if you had a child) and why?
Yes, because the more money saved up means less money we would have to pay in the future. Paying later on would be a lot worse, especially for a freshly graduated student trying to find job.
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.
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
System 1: Since this system had niether the same y-intercept or slope there is only one solution it will have which is, in this case, (4,5).
System 2: This system has equations that has the same slope resulting in parallel lines. Therefore, there is no solution.
System 3: This system of equations contains the same slope and y-intercept making it the same line. It has infinite 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.
Elimination:
Substitution:
Graphing: Used when we are given a set of equations where it is in slope-intercept form
Special Trick: CHECK ANSWERS.. plug in the variables to an equation.
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)= 75x + 1050
- What is the y-intercept of each function? Explain in the context of the situation. : Y-intercept of each function means the amount of money that a person deposit to their account.
- What is the slope of each function? Explain in the context of the situation.: The slope of the blue function 100x and 75x for the red. The slope of the function is the additional amount of money added at the end of each year
- Which account is better? Is this always true? Be specific, using dates and account values from the graph to support your argument.
After the first year the blue account was better because it saved more money, faster. However, the red account did start out with a little more money than the blue account.- Which account would you choose when opening to save up for your college in a few years and why?
I would choose the blue account because I would want to make sure we would have enough money saved up as possible.- Would you choose that same account to start your child's college fund (if you had a child) and why?
Yes, because the more money saved up means less money we would have to pay in the future. Paying later on would be a lot worse, especially for a freshly graduated student trying to find job.