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3.3 Writing Linear Equations (In Linear Form)

Last updated 10 months 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
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.
1
How many $5 bills are in the piggy bank if there are no $10 bills?_______
1
How many $10 bills are there if there are no $5 bills?_______
1

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

1

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

1

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.

Learn It
This is on your Notes Paper: Write answers in formative, and on your notes pages for reference.
3
Equation: 3x + 5y = 30
A=_______
B=_______
C=_______
3
Equation: 4x - 7y = 12
A=_______
B=_______
C=_______
1
A = 4
B = 2
C = 24
Equation:_______
1
A = 3
B = -2
C = 18
Equation: _______
Learn It & Practice It in Desmos: Writing Equations in Standard Form
Learn It #2 (after Desmos)
3

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

  • 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.
1

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

1

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

1

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

1

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

Practice It 2
Graphing Practice
Find the x and y intercepts and plot the line on the graph.
3

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

  • 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.
3

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

  • 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.
3

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

  • 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