3.3 Writing Linear Equations (In Linear Form)

Last updated about 1 year ago

17 questions

Note from the author:

OBJECTIVES & STANDARDS
Math Objectives
Define quantities in a word problem algebraically
Generate standard form equations from word problems
Graph standard form equations on the coordinate plane
Interpret the meaning of intercepts and intersections
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP1
CCSS.PRACTICE.MP4
CCSS.PRACTICE.MP7
CCSS.HSF.BF.A.1
CCSS.HSF.IF.B.4
CCSS.HSA.CED.A.2
Personal Finance Objectives
Quantify financial constraints
Evaluate trade-offs in spending and budgeting choices
National Standards for Personal Financial Education
Saving
9a: Explain how external influences (e.g. peers, family, or social media) can impact personal savings decisions
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems

Instructions

OBJECTIVES & STANDARDS
Math Objectives
Define quantities in a word problem algebraically
Generate standard form equations from word problems
Graph standard form equations on the coordinate plane
Interpret the meaning of intercepts and intersections
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP1
CCSS.PRACTICE.MP4
CCSS.PRACTICE.MP7
CCSS.HSF.BF.A.1
CCSS.HSF.IF.B.4
CCSS.HSA.CED.A.2
Personal Finance Objectives
Quantify financial constraints
Evaluate trade-offs in spending and budgeting choices
National Standards for Personal Financial Education
Saving
9a: Explain how external influences (e.g. peers, family, or social media) can impact personal savings decisions
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems

Intro - Warm-Up

Learn It

Learn It & Practice It in Desmos: Writing Equations in Standard Form

Practice It 2

Explore It: Desmos 2: Linear Equations in Standard Form Updated

3.3 Writing Linear Equations (In Linear Form)

Last updated about 1 year ago

17 questions

Note from the author:

OBJECTIVES & STANDARDS
Math Objectives
Define quantities in a word problem algebraically
Generate standard form equations from word problems
Graph standard form equations on the coordinate plane
Interpret the meaning of intercepts and intersections
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP1
CCSS.PRACTICE.MP4
CCSS.PRACTICE.MP7
CCSS.HSF.BF.A.1
CCSS.HSF.IF.B.4
CCSS.HSA.CED.A.2
Personal Finance Objectives
Quantify financial constraints
Evaluate trade-offs in spending and budgeting choices
National Standards for Personal Financial Education
Saving
9a: Explain how external influences (e.g. peers, family, or social media) can impact personal savings decisions
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems

Instructions

OBJECTIVES & STANDARDS
Math Objectives
Define quantities in a word problem algebraically
Generate standard form equations from word problems
Graph standard form equations on the coordinate plane
Interpret the meaning of intercepts and intersections
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP1
CCSS.PRACTICE.MP4
CCSS.PRACTICE.MP7
CCSS.HSF.BF.A.1
CCSS.HSF.IF.B.4
CCSS.HSA.CED.A.2
Personal Finance Objectives
Quantify financial constraints
Evaluate trade-offs in spending and budgeting choices
National Standards for Personal Financial Education
Saving
9a: Explain how external influences (e.g. peers, family, or social media) can impact personal savings decisions
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems

Intro - Warm-Up

CALCULATE: Piggy Bank Math
Andre gets paid $5 a week for his allowance and $10 every time he mows his neighbor’s yard. He puts all his money into his piggy bank. His piggy bank contains $70 and has only $5 bills and $10 bills.

How many $5 bills are in the piggy bank if there are no $10 bills?_______ 

How many $10 bills are there if there are no $5 bills?_______ 

Learn It

This is on your Notes Paper:  Write answers in formative, and on your notes pages for reference. 

Equation:  3x + 5y = 30
A=_______ 
B=_______ 
C=_______ 

Equation: 4x - 7y = 12
A=_______ 
B=_______ 
C=_______ 

A = 4
B = 2
C = 24
Equation:_______ 

Learn It & Practice It in Desmos: Writing Equations in Standard Form

Learn It #2 (after Desmos)

What is the real-world meaning of the y-intercept in this example?

What is the real-world meaning of the x-intercept in this example?

What is easy to see in slope-intercept form but is not so obvious in standard form?

Practice It 2

Graphing Practice
Find the x and y intercepts and plot the line on the graph.

Graph 2x - 6y = 18
Check your answer in desmos: Screen shot desmos in Show your work.

Instructions

Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
After you have plotted all graphs, click on x or y intercept tab to graph the intercepts.

Explore It: Desmos 2: Linear Equations in Standard Form Updated

Complete:
Desmos #2 Linear Equations in Standard Form 
Desmos #3: Card Sort
Desmos #4:  Writing and Graphing a System of Linear Equations

3.3 Writing Linear Equations (In Linear Form)

3.3 Writing Linear Equations (In Linear Form)

What is the real-world meaning of the y-intercept in this example?

What is the real-world meaning of the x-intercept in this example?

What is easy to see in slope-intercept form but is not so obvious in standard form?

Graph 2x - 6y = 18
Check your answer in desmos: Screen shot desmos in Show your work.

Rebekah guessed that the piggy bank contained five $5 bills. Could she be right? Why or why not?

Describe in words how you would solve for the number of $10 bills if there are exactly eight $5 bills in the piggy bank.

Write an equation using variables that models the total value of the piggy bank based on the number of $5 bills and $10 bills inside. Use your description to help.

For Equation: 5x+10y=70
Plot the two intercepts and draw the line connecting them.
y-Intercept = (0,7)
x-Intercept=(14,0)

What is the real-world meaning of the y-intercept in this example?

What is the real-world meaning of the x-intercept in this example?

What is easy to see in slope-intercept form but is not so obvious in standard form?

What is easier to find using the standard form than using slope-intercept form?

Graph 2x - 6y = 18
Check your answer in desmos: Screen shot desmos in Show your work.

Graph: 9x + 2y = 18
Check your answer in desmos: Screen shot desmos in Show your work.

Graph: -4x - 8y = 12
Check your answer in desmos: Screen shot desmos in Show your work.

Rebekah guessed that the piggy bank contained five $5 bills. Could she be right? Why or why not?

Describe in words how you would solve for the number of $10 bills if there are exactly eight $5 bills in the piggy bank.

Write an equation using variables that models the total value of the piggy bank based on the number of $5 bills and $10 bills inside. Use your description to help.

For Equation: 5x+10y=70
Plot the two intercepts and draw the line connecting them.
y-Intercept = (0,7)
x-Intercept=(14,0)

What is easier to find using the standard form than using slope-intercept form?

Graph: 9x + 2y = 18
Check your answer in desmos: Screen shot desmos in Show your work.

Graph: -4x - 8y = 12
Check your answer in desmos: Screen shot desmos in Show your work.

3.3 Writing Linear Equations (In Linear Form)

3.3 Writing Linear Equations (In Linear Form)

What is the real-world meaning of the y-intercept in this example?

What is the real-world meaning of the x-intercept in this example?

What is easy to see in slope-intercept form but is not so obvious in standard form?

Graph 2x - 6y = 18Check your answer in desmos: Screen shot desmos in Show your work.

Rebekah guessed that the piggy bank contained five $5 bills. Could she be right? Why or why not?

Describe in words how you would solve for the number of $10 bills if there are exactly eight $5 bills in the piggy bank.

Write an equation using variables that models the total value of the piggy bank based on the number of $5 bills and $10 bills inside. Use your description to help.

For Equation: 5x+10y=70Plot the two intercepts and draw the line connecting them.y-Intercept = (0,7)x-Intercept=(14,0)

What is the real-world meaning of the y-intercept in this example?

What is the real-world meaning of the x-intercept in this example?

What is easy to see in slope-intercept form but is not so obvious in standard form?

What is easier to find using the standard form than using slope-intercept form?

Graph 2x - 6y = 18Check your answer in desmos: Screen shot desmos in Show your work.

Graph: 9x + 2y = 18Check your answer in desmos: Screen shot desmos in Show your work.

Graph: -4x - 8y = 12Check your answer in desmos: Screen shot desmos in Show your work.

Rebekah guessed that the piggy bank contained five $5 bills. Could she be right? Why or why not?

Describe in words how you would solve for the number of $10 bills if there are exactly eight $5 bills in the piggy bank.

Write an equation using variables that models the total value of the piggy bank based on the number of $5 bills and $10 bills inside. Use your description to help.

For Equation: 5x+10y=70Plot the two intercepts and draw the line connecting them.y-Intercept = (0,7)x-Intercept=(14,0)

What is easier to find using the standard form than using slope-intercept form?

Graph: 9x + 2y = 18Check your answer in desmos: Screen shot desmos in Show your work.

Graph: -4x - 8y = 12Check your answer in desmos: Screen shot desmos in Show your work.

Graph 2x - 6y = 18
Check your answer in desmos: Screen shot desmos in Show your work.

For Equation: 5x+10y=70
Plot the two intercepts and draw the line connecting them.
y-Intercept = (0,7)
x-Intercept=(14,0)

Graph 2x - 6y = 18
Check your answer in desmos: Screen shot desmos in Show your work.

Graph: 9x + 2y = 18
Check your answer in desmos: Screen shot desmos in Show your work.

Graph: -4x - 8y = 12
Check your answer in desmos: Screen shot desmos in Show your work.

For Equation: 5x+10y=70
Plot the two intercepts and draw the line connecting them.
y-Intercept = (0,7)
x-Intercept=(14,0)

Graph: 9x + 2y = 18
Check your answer in desmos: Screen shot desmos in Show your work.

Graph: -4x - 8y = 12
Check your answer in desmos: Screen shot desmos in Show your work.