2.07BM Graphing Linear Equations (2/24/2025)

Last updated 10 months ago

32 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

Akwankyerɛ

Intro (Warm-Up)

Learn It

Application Problems

Application Level 2

Application Level 3 *Bonus, not required*

2.07BM Graphing Linear Equations (2/24/2025)

Last updated 10 months ago

32 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

OBJECTIVES & STANDARDS

Math Objectives

Graph a linear equation using slope-intercept form
Make connections between sign and size of slope and the graph

Common Core Math Standards

Personal Finance Objective

Apply linear equations to real-world wage scenarios

National Standards for Personal Financial Education

Earning Income

4b: Explain why wages or salaries vary among employees in different types of jobs and among workers in the same jobs
5a: Discuss how economic and labor market conditions can affect income, career opportunities, and employment status

DISTRIBUTION & PLANNING

Distribute to students

Student Activity Packet
Application Problems
Salary Cards (see Application Key for directions

Akwankyerɛ

OBJECTIVES & STANDARDS

Math Objectives

Graph a linear equation using slope-intercept form
Make connections between sign and size of slope and the graph

Common Core Math Standards

Personal Finance Objective

Apply linear equations to real-world wage scenarios

National Standards for Personal Financial Education

Earning Income

4b: Explain why wages or salaries vary among employees in different types of jobs and among workers in the same jobs
5a: Discuss how economic and labor market conditions can affect income, career opportunities, and employment status

DISTRIBUTION & PLANNING

Distribute to students

Student Activity Packet
Application Problems
Salary Cards (see Application Key for directions

Intro (Warm-Up)

COMPARE: ATM Fees

Many banks charge for out of network ATM use. Out of network ATMs are ones provided by someone other than your bank. While you’re away at college, you will have to rely on these out of network ATMs if your local bank does not have a branch near your school.

Compare the following checking account fee structures.

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Which bank offers a better fee structure for a month of usage? Describe your reasons.

Is one bank ALWAYS better? What factors might affect which bank has the better fee structure?

Learn It

EXAMPLE: Graphing Linear Equations Using Slope-Intercept Form (Video Walkthrough)

Review the example completed problem below. You can see it modeled here

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Akwankyerɛ

Klik Graph tab (Graph 1, Graph 2, ne nea ɛkeka ho) so ma graph biara a ɛsɛ sɛ wobɔ.
Klik graph no akyi na fa asɛm bi ka ho. Fa nsɛntitiriw abien ka ho na yɛ graph. Twe asɛm bi anaa kyerɛw x ne y coordinates na sesa ne gyinabea. Klik asɛm bi so na popa.
Sɛ wobɔ wo graph no wie a, wubetumi ahyɛ dashed line box no mu.
Sɛ woyɛ graphs nyinaa wie a, klik x anaa y intercept tab so na yɛ intercepts no graph.

Akwankyerɛ

Klik Graph tab (Graph 1, Graph 2, ne nea ɛkeka ho) so ma graph biara a ɛsɛ sɛ wobɔ.
Klik graph no akyi na fa asɛm bi ka ho. Fa nsɛntitiriw abien ka ho na yɛ graph. Twe asɛm bi anaa kyerɛw x ne y coordinates na sesa ne gyinabea. Klik asɛm bi so na popa.
Sɛ wobɔ wo graph no wie a, wubetumi ahyɛ dashed line box no mu.
Sɛ woyɛ graphs nyinaa wie a, klik x anaa y intercept tab so na yɛ intercepts no graph.

Akwankyerɛ

Klik Graph tab (Graph 1, Graph 2, ne nea ɛkeka ho) so ma graph biara a ɛsɛ sɛ wobɔ.
Klik graph no akyi na fa asɛm bi ka ho. Fa nsɛntitiriw abien ka ho na yɛ graph. Twe asɛm bi anaa kyerɛw x ne y coordinates na sesa ne gyinabea. Klik asɛm bi so na popa.
Sɛ wobɔ wo graph no wie a, wubetumi ahyɛ dashed line box no mu.
Sɛ woyɛ graphs nyinaa wie a, klik x anaa y intercept tab so na yɛ intercepts no graph.

Akwankyerɛ

Klik Graph tab (Graph 1, Graph 2, ne nea ɛkeka ho) so ma graph biara a ɛsɛ sɛ wobɔ.
Klik graph no akyi na fa asɛm bi ka ho. Fa nsɛntitiriw abien ka ho na yɛ graph. Twe asɛm bi anaa kyerɛw x ne y coordinates na sesa ne gyinabea. Klik asɛm bi so na popa.
Sɛ wobɔ wo graph no wie a, wubetumi ahyɛ dashed line box no mu.
Sɛ woyɛ graphs nyinaa wie a, klik x anaa y intercept tab so na yɛ intercepts no graph.

Akwankyerɛ

Klik Graph tab (Graph 1, Graph 2, ne nea ɛkeka ho) so ma graph biara a ɛsɛ sɛ wobɔ.
Klik graph no akyi na fa asɛm bi ka ho. Fa nsɛntitiriw abien ka ho na yɛ graph. Twe asɛm bi anaa kyerɛw x ne y coordinates na sesa ne gyinabea. Klik asɛm bi so na popa.
Sɛ wobɔ wo graph no wie a, wubetumi ahyɛ dashed line box no mu.
Sɛ woyɛ graphs nyinaa wie a, klik x anaa y intercept tab so na yɛ intercepts no graph.

Akwankyerɛ

Klik Graph tab (Graph 1, Graph 2, ne nea ɛkeka ho) so ma graph biara a ɛsɛ sɛ wobɔ.
Klik graph no akyi na fa asɛm bi ka ho. Fa nsɛntitiriw abien ka ho na yɛ graph. Twe asɛm bi anaa kyerɛw x ne y coordinates na sesa ne gyinabea. Klik asɛm bi so na popa.
Sɛ wobɔ wo graph no wie a, wubetumi ahyɛ dashed line box no mu.
Sɛ woyɛ graphs nyinaa wie a, klik x anaa y intercept tab so na yɛ intercepts no graph.

Graph the following equations:
Graph 1: y=2x+1
Graph 2: y=-2x+1
Graph 3: y=1/2x+1
Graph 4: y=-1/2x+1

Akwankyerɛ

Klik Graph tab (Graph 1, Graph 2, ne nea ɛkeka ho) so ma graph biara a ɛsɛ sɛ wobɔ.
Klik graph no akyi na fa asɛm bi ka ho. Fa nsɛntitiriw abien ka ho na yɛ graph. Twe asɛm bi anaa kyerɛw x ne y coordinates na sesa ne gyinabea. Klik asɛm bi so na popa.
Sɛ wobɔ wo graph no wie a, wubetumi ahyɛ dashed line box no mu.

Graph the following equations:

Akwankyerɛ

Klik Graph tab (Graph 1, Graph 2, ne nea ɛkeka ho) so ma graph biara a ɛsɛ sɛ wobɔ.
Klik graph no akyi na fa asɛm bi ka ho. Fa nsɛntitiriw abien ka ho na yɛ graph. Twe asɛm bi anaa kyerɛw x ne y coordinates na sesa ne gyinabea. Klik asɛm bi so na popa.
Sɛ wobɔ wo graph no wie a, wubetumi ahyɛ dashed line box no mu.

Compare graphs in your group.
How does the sign of the slope affect the graph of the equation?
How does the size of the slope change the graph of the equation?

Application Problems

Comparing Compensation

Congratulations on being hired! Please flip over your wage card to see how much you’ll be making at your new job. On your first day, you’re discussing your compensation with the other new hires in your group.

Part 1: Equations

Write an equation that represents each team member’s compensation. Your equation should represent a relationship between hours worked (x) and total pay (y). Please put the equation for each team member in the boxes below.

Team Member 1

Team Member 2

Team Member 3

Using the equations that you wrote, who do you think got the best compensation deal?
What does the slope represent in each equation?
What does the y-intercept represent in each equation?

*If present, please do this on your paper in your notebook. If absent, this is your make up work. *

Part 1: Equations

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Write an equation that represents each team member’s compensation. Your equation should represent a relationship between hours worked (x) and total pay (y). Please put the equation for each team member in the boxes below.

Team Member 1

Team Member 2

Team Member 3

Using the equations that you wrote, who do you think got the best compensation deal?
What does the slope represent in each equation?
What does the y-intercept represent in each equation?

Part 3: Reflect

Well done! Your final task is to answer the questions below. You can use either the equations or the graph to help you complete the questions.

Application Level 2

Part 1: Minimum Wage

Minimum wage is the lowest hourly wage that an employer can pay you. Each state sets its own minimum wage but that wage must be at least $7.25 per hour, which is the national minimum wage set by the federal government.

What is the minimum wage in your state? Visit MinimumWage.com and write your answer below.

What is the average monthly rent in your state? Visit World Population Review and write your answer below.

Application Level 3 *Bonus, not required*

A Living Wage

Visit MIT Living Wage Calculator
Click your state
Click your county

Consider each of the households living in your county.

Family 1: A married couple with one child: Due to the high cost of childcare, one parent stays home to care for the child while the other works 40 hours per week making $18 per hour. They also receive a monthly stipend of $50 to cover work related expenses.
Family 2: A married couple with two children who are in school. Both adults are working 40 hours per week with one making $16 per hour while the other makes minimum wage. One of these workers pays $25 per month in union dues.
Family 3: A fulltime student who only has the time to work 20 hours per week making $2 more than the minimum wage. They have a gerbil as a pet.

Part 1: Equations

Write an equation for the monthly wages of each family, including any bonuses or wage reduction.

Family 1

Family 2

Family 3

Part 3: Reflect
A living wage is defined as “the hourly rate that an individual in a household must earn to support his or herself and their family.” Using the information provided on the MIT Living Wage Calculator, do any of the families make enough to earn a living wage?

Based on the Typical Expenses section for your county on the MIT Living Wage Calculator, how many hours does each family need to work per month to cover housing expenses. (Note that the values in Typical Expenses section are ANNUAL expenses, so you will need to divide by 12 to get MONTHLY expense

2.07BM Graphing Linear Equations (2/24/2025)

2.07BM Graphing Linear Equations (2/24/2025)

Which bank offers a better fee structure for a month of usage? Describe your reasons.

Is one bank ALWAYS better? What factors might affect which bank has the better fee structure?

Graph the following equations: Graph 1: y=2x+1Graph 2: y=-2x+1Graph 3: y=1/2x+1Graph 4: y=-1/2x+1

Graph the following equations:

Compare graphs in your group. How does the sign of the slope affect the graph of the equation?How does the size of the slope change the graph of the equation?

What is the minimum wage in your state? Visit MinimumWage.com and write your answer below.

What is the average monthly rent in your state? Visit World Population Review and write your answer below.

Part 3: ReflectA living wage is defined as “the hourly rate that an individual in a household must earn to support his or herself and their family.” Using the information provided on the MIT Living Wage Calculator, do any of the families make enough to earn a living wage?

Based on the Typical Expenses section for your county on the MIT Living Wage Calculator, how many hours does each family need to work per month to cover housing expenses. (Note that the values in Typical Expenses section are ANNUAL expenses, so you will need to divide by 12 to get MONTHLY expense

Which bank offers a better fee structure for a month of usage? Describe your reasons.

Is one bank ALWAYS better? What factors might affect which bank has the better fee structure?

How could you avoid these fees if you are away at school without access to a local branch?

Find a partner and discuss your bank choices. Write down how you could best compare the two fee structures.

https://drive.google.com/file/d/1APJT1T-DMD_bCu_ooTSrgeFDfvqaG68F/viewAfter viewing this graph, how does the graph help you analyze the bank fees?

Graph the equation: y= - 3x

y=x - 5

Graph the following equations: Graph 1: y=2x+1Graph 2: y=-2x+1Graph 3: y=1/2x+1Graph 4: y=-1/2x+1

Graph the following equations:

Compare graphs in your group. How does the sign of the slope affect the graph of the equation?How does the size of the slope change the graph of the equation?

*We found this difficult to graph in Formative& Desmos due to the size of the graph. Please refer to the picture below for reference and answer questions 19-27.

If each team member works 30 hours next week, which member of your team has the best compensation package?

During which range of hours is each team member’s compensation package the most beneficial? (For example: “From 10 hours to 18 hours, Team Member 99 makes the most money”)

What is the minimum wage in your state? Visit MinimumWage.com and write your answer below.

What is the average monthly rent in your state? Visit World Population Review and write your answer below.

Write an equation for your state’s minimum wage where x represents hours worked and y represents total pay.

There have been proposals to increase the federal minimum wage to $15 per hour. Write an equation for representing a $15 minimum wage where x represents hours worked and y represents total pay

How many more hours would you need to work to pay rent if the minimum wage was to $7.25 per hour?

A common guideline given by financial advisors is that you should spend no more than 30% of your gross income on rent. Assume you work 160 hours per month (~40 hours per week). What percentage of pay is being used to pay for rent in your state if you make:Minimum wage?$15 per hour?

Part 2: GraphGraph each equation on the same grid, using different colors to represent each family.

Part 3: ReflectA living wage is defined as “the hourly rate that an individual in a household must earn to support his or herself and their family.” Using the information provided on the MIT Living Wage Calculator, do any of the families make enough to earn a living wage?

Based on the Typical Expenses section for your county on the MIT Living Wage Calculator, how many hours does each family need to work per month to cover housing expenses. (Note that the values in Typical Expenses section are ANNUAL expenses, so you will need to divide by 12 to get MONTHLY expense

Family 1 and Family 2’s lines intersect. What does that intersection represent in the context of hours worked and wages?

How could you avoid these fees if you are away at school without access to a local branch?

Find a partner and discuss your bank choices. Write down how you could best compare the two fee structures.

https://drive.google.com/file/d/1APJT1T-DMD_bCu_ooTSrgeFDfvqaG68F/viewAfter viewing this graph, how does the graph help you analyze the bank fees?

Graph the equation: y= - 3x

y=x - 5

*We found this difficult to graph in Formative& Desmos due to the size of the graph. Please refer to the picture below for reference and answer questions 19-27.

If each team member works 30 hours next week, which member of your team has the best compensation package?

During which range of hours is each team member’s compensation package the most beneficial? (For example: “From 10 hours to 18 hours, Team Member 99 makes the most money”)

Write an equation for your state’s minimum wage where x represents hours worked and y represents total pay.

There have been proposals to increase the federal minimum wage to $15 per hour. Write an equation for representing a $15 minimum wage where x represents hours worked and y represents total pay

How many more hours would you need to work to pay rent if the minimum wage was to $7.25 per hour?

A common guideline given by financial advisors is that you should spend no more than 30% of your gross income on rent. Assume you work 160 hours per month (~40 hours per week). What percentage of pay is being used to pay for rent in your state if you make:Minimum wage?$15 per hour?

Part 2: GraphGraph each equation on the same grid, using different colors to represent each family.

Family 1 and Family 2’s lines intersect. What does that intersection represent in the context of hours worked and wages?

Graph the following equations:
Graph 1: y=2x+1
Graph 2: y=-2x+1
Graph 3: y=1/2x+1
Graph 4: y=-1/2x+1

Compare graphs in your group.
How does the sign of the slope affect the graph of the equation?
How does the size of the slope change the graph of the equation?

Part 3: Reflect
A living wage is defined as “the hourly rate that an individual in a household must earn to support his or herself and their family.” Using the information provided on the MIT Living Wage Calculator, do any of the families make enough to earn a living wage?

https://drive.google.com/file/d/1APJT1T-DMD_bCu_ooTSrgeFDfvqaG68F/view
After viewing this graph, how does the graph help you analyze the bank fees?

Graph the following equations:
Graph 1: y=2x+1
Graph 2: y=-2x+1
Graph 3: y=1/2x+1
Graph 4: y=-1/2x+1

Compare graphs in your group.
How does the sign of the slope affect the graph of the equation?
How does the size of the slope change the graph of the equation?

A common guideline given by financial advisors is that you should spend no more than 30% of your gross income on rent. Assume you work 160 hours per month (~40 hours per week). What percentage of pay is being used to pay for rent in your state if you make:
Minimum wage?
$15 per hour?

Part 2: Graph
Graph each equation on the same grid, using different colors to represent each family.

Part 3: Reflect
A living wage is defined as “the hourly rate that an individual in a household must earn to support his or herself and their family.” Using the information provided on the MIT Living Wage Calculator, do any of the families make enough to earn a living wage?

https://drive.google.com/file/d/1APJT1T-DMD_bCu_ooTSrgeFDfvqaG68F/view
After viewing this graph, how does the graph help you analyze the bank fees?

A common guideline given by financial advisors is that you should spend no more than 30% of your gross income on rent. Assume you work 160 hours per month (~40 hours per week). What percentage of pay is being used to pay for rent in your state if you make:
Minimum wage?
$15 per hour?

Part 2: Graph
Graph each equation on the same grid, using different colors to represent each family.