2.1: 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.
The relationship between different pair of lines and their slope is that they could be different and still intersect each other. In graph 1 the slopes are similar but the lines dont intersect each other causing it to have no solution. In graph 2 the slope are the same and the 2 lines intersect each other at point (5.5,8) with only one soultion. In graph 3 there is no slope because the lines are equal making it have all 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.
1. Graphing- one solution; where the two lines me ( they cross ) no solution; parallel same slope and a different y-intercept ( they dont cross ) indefinite; many same y-intercept and slope. ( same line ) 2. Elimination- both equations are in standard form 3. Substitution- has atleast one variable by itself.
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. B(t)= 1050+ 75t 2. The y-intercept of the blue linear function is 1000 and the y-intercept of the red linear function is 1050. They are the starting depoites. 3. The slope of the red function is 75 and the slope of the blue function is 100 because its an additional deposite that the person is depositing. 4. The red linear function is the better account because your not depositing as much money so you can have some money to spend then to put it all away. No, its not always true because you could always change up your deposite and put as much money as you want in. 5. I would chose the blue linear function because the more i save up the sooner i can pay off all my college bills then having to be behind because im still saving up. 6. No, i would go back to the red linear function because throughout the years that my child is growing up i have enough time to cover all the payments and take care of them.
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.
The relationship between different pair of lines and their slope is that they could be different and still intersect each other. In graph 1 the slopes are similar but the lines dont intersect each other causing it to have no solution. In graph 2 the slope are the same and the 2 lines intersect each other at point (5.5,8) with only one soultion. In graph 3 there is no slope because the lines are equal making it have all 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.
1. Graphing- one solution; where the two lines me ( they cross )
no solution; parallel same slope and a different y-intercept ( they dont cross )
indefinite; many same y-intercept and slope. ( same line )
2. Elimination- both equations are in standard form
3. Substitution- has atleast one variable by itself.
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:
1. B(t)= 1050+ 75t
2. The y-intercept of the blue linear function is 1000 and the y-intercept of the red linear function is 1050. They are the starting depoites.
3. The slope of the red function is 75 and the slope of the blue function is 100 because its an additional deposite that the person is depositing.
4. The red linear function is the better account because your not depositing as much money so you can have some money to spend then to put it all away. No, its not always true because you could always change up your deposite and put as much money as you want in.
5. I would chose the blue linear function because the more i save up the sooner i can pay off all my college bills then having to be behind because im still saving up.
6. No, i would go back to the red linear function because throughout the years that my child is growing up i have enough time to cover all the payments and take care of them.