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.
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(finding a solution) to a system of equations are substitution, combination, and graphing. Substitution method is where you plug in for the x or y values, depending on which variable they give you. Combination method is when you combine variables to cancel each other out to solve for another variable. Graphing is when you graph both equations to find the solution. It is necessary to choose substitution over combination and graphing when they give you the value of a variable. Once they give you the value, all you need to do is plug in to solve for the other variable. It is necessary to choose combination over substitution and graphing when there are no given values for the variables, and when the system has no fractions involved. Its necessary to choose graphing over combination and substitution when the system of equation consists of fractions, and when its already written in slope-intercept form. What i look for are fractions, systems of equations written in slope-intercept form, or values or the variables.
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.red : f(x)= 75x+1050
2.y-intercept of red = 1050 In context, the y-intercept of each function is the fixed amount of money deposited to start of the account.
y-intercept of blue = 1000
slope of red: 75 In context, the slope of each function represents the amount of money deposited at the end of each year.
slope of blue: 100
Unit 2: Systems of Equations
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.
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.
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(finding a solution) to a system of equations are substitution, combination, and graphing. Substitution method is where you plug in for the x or y values, depending on which variable they give you. Combination method is when you combine variables to cancel each other out to solve for another variable. Graphing is when you graph both equations to find the solution. It is necessary to choose substitution over combination and graphing when they give you the value of a variable. Once they give you the value, all you need to do is plug in to solve for the other variable. It is necessary to choose combination over substitution and graphing when there are no given values for the variables, and when the system has no fractions involved. Its necessary to choose graphing over combination and substitution when the system of equation consists of fractions, and when its already written in slope-intercept form. What i look for are fractions, systems of equations written in slope-intercept form, or values or the variables.
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.red : f(x)= 75x+1050
2.y-intercept of red = 1050 In context, the y-intercept of each function is the fixed amount of money deposited to start of the account.
y-intercept of blue = 1000
slope of red: 75 In context, the slope of each function represents the amount of money deposited at the end of each year.
slope of blue: 100