today’s agenda e – e – how do you rewrite equations from standard form to slope-intercept...
TRANSCRIPT
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Today’s AgendaE – E – How do you rewrite equations from standard form to
slope-intercept form?A - A - Warm-up: Writing systems equations
Journal: Describe 2 ways to graph a lineReview: Looking at y=mx+b
T - T - New: Rewriting equations from standard to slope-intercept form (graphic organizer)Classwork: Racing Game
S – S – Journal writing to answer LEQHomework: Rewriting Equations worksheet
104/21/23 Geometry CP
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JOURNAL TIME (8 mins)
Directions: Write down the journal prompt and then answer
Describe the 2 different ways to graph a line that we have learned in class so far (Be specific)
Which way do you prefer and why?
04/21/23 Geometry CP 2
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Rewriting Equations Rewriting Equations
LLesson EEssential QQuestion:
How do you rewrite equations from standard form to graphing form?
04/21/23 3Geometry CP
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2 Forms of Linear Equations 2 Forms of Linear Equations
The forms of linear equations are the formats in which the information is written in.
These two forms are the most commonly used ways to write linear equations.
1. Standard Form: Ax + By =C
2. Slope Intercept Form: y=mx+b
04/21/23 Geometry CP 4
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Important!!! Important!!! This is one of the BIG concepts you
learned in Algebra I. You need to thoroughly understand this!
Slope – Intercept Form
y = mx + b
m represents the slope
b represents the y-intercept
04/21/23 Geometry CP 5
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Write the equation of a line that has a y-intercept of - 3 and a slope of - 4.
y = -3x – 4
y = -4x – 3
y = -3x + 4
y = -4x + 3
Review: -Review: -Writing Equations Writing Equations Given Slope & Y-interceptGiven Slope & Y-intercept
04/21/23 Geometry CP 6
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Review: Find the slope and y-intercept of y = 4 – 2x
m = 2; b = 4
m = 4; b = 2
m = -2; b = 4
m = 4; b = -2
04/21/23 Geometry CP 7
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Standard Form to Slope Intercept Form
Ax + By = C
to
y = mx + b04/21/23 Geometry CP 8
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What is Standard Form
• Standard Form is Ax + By = C
• Basically, if your x and y are on the same side of the equation, then it is in standard form.
04/21/23 Geometry CP 9
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Identify the equations in standard form
A. 2x – 4y = 6
B. y = 3x + 1
C. x – y = 1
D. 4y = 5x + 8
E. -x + 2y = 6
F. y = 1/3x + 2.5
G. 2y +7 = 3x
04/21/23 Geometry CP 10
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Converting from Converting from standard formstandard form (Ax + By = C) (Ax + By = C) to to slope-intercept formslope-intercept form (y = mx + b) (y = mx + b)
04/21/23 Geometry CP 11
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Converting Standard to Slope-Intercept form
2x + 3y = 62x + 3y = 6 ax + by = cax + by = c
-2x-2x -2x-2x 3y = 6 - 2x3y = 6 - 2x
33 33 33
y = 2 -y = 2 - 22
33xx
y = - + 2y = - + 22233
xx y = mx + by = mx + b
WE WANT THIS FORM!!!WE WANT THIS FORM!!!
(Standard Form)(Standard Form)
(Slope- Intercept)(Slope- Intercept)
04/21/23 Geometry CP 12
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3 Powerful Moves to get your equation into y=
1. MOVE X2. DROP ALL3. DIVIDE ALL
6X + 4Y = 12
04/21/23 Geometry CP 13
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1. MOVE X Add or Subtract the x
term to the other side of equals.
6X + 4Y = 12
6X + 4Y = 12 -6x -6x
3 Powerful Moves to get your equation into y=
04/21/23 Geometry CP 14
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2. DROP ALLBring all terms down in
order.
Do not add or subtract unlike terms!!!
6X + 4Y = 12
6X + 4Y = 12 -6x -6x
4y = 12 -6x
3 Powerful Moves to get your equation into y=
04/21/23 Geometry CP 15
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3. DIVIDE ALLDivide each term by
the number attached to y
keep slope a fraction!
6X + 4Y = 12
6X + 4Y = 12 -6x -6x
4y = 12 -6x 4 4 4 y= 3 – 3/2
x
2
3 Powerful Moves to get your equation into y=
04/21/23 Geometry CP 16
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1. MOVE X2. DROP ALL3. DIVIDE ALL
-4X + 3Y = 12
3 Powerful Moves to get your equation into y=
04/21/23 Geometry CP 17
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1. MOVE X Add or Subtract the x
term to the other side of equals.
-4X + 3Y = 12
-4X + 3Y = 12 +4x
+4x
3 Powerful Moves to get your equation into y=
04/21/23 Geometry CP 18
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2. DROP ALLBring all terms down in
order.
Do not add or subtract unlike terms!!!
-4X + 3Y = 12
-4X + 3Y = 12 +4x +4x
3y = 12 +4x
3 Powerful Moves to get your equation into y=
04/21/23 Geometry CP 19
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3. DIVIDE ALLDivide each term by
the number attached to y
keep slope a fraction!
-4X + 3Y = 12
-4X + 3Y = 12 +4x +4x
3y = 12 +4x 3 3 3 y= 4 + 4/3
x
2
3 Powerful Moves to get your equation into y=
04/21/23 Geometry CP 20
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The 3 Power Moves to getting linesinto y = form.
1. 2. 3.
MOVE the x term by Adding/Subtracting!
Drop ALL!
Divide ALL!
04/21/23 Geometry CP 21
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Pair Race Directions
Equations are going to flash on the screen. The first one to step forward and describe the first step to converting the equation will earn the point.
First person to answer correctly wins!
Everyone….Please pay attention
04/21/23 Geometry CP 22
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Example
3x + 2y = 18
The first step is: Subtract 3x from both sides
That would look like:
3x + 2y = 18
-3x -3x
2y = 18 – 3x04/21/23 Geometry CP 23
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Example
-7x + 14y = 28
The first step is: Add 7x to both sides
That would look like:
-7x + 14y = 28
+7x +7x
14y = 28 + 7x 04/21/23 Geometry CP 24
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Let’s Race!
• As quickly and quietly as possible line up please!
• No hitting, touching, pushing, poking…just get in line!
Ready, Set, GO!!04/21/23 Geometry CP 25
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4x + 5y = 10Correct! Subtract 4x from both sides!!
Great Job!
4x + 5y = 10 -4x -4x
5y = 10 – 4x 04/21/23 Geometry CP 26
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-6x + 3y = 12Correct! Add 6x to both sides!!
Great Job!
-6x + 3y = 12 +6x +6x
3y = 12 + 6x 04/21/23 Geometry CP 27
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9x - y = -8Correct! Subtract 9x from both sides!!
Great Job!
9x - y = -8 -9x -9x
- y = -8 – 9x 04/21/23 Geometry CP 28
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10x - 20y = 20Correct! Subtract 10x from both sides!!
Great Job!
10x - 20y = 20 -10x -10x
-20y = 20 – 10x 04/21/23 Geometry CP 29
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-11x + 11y = 33Correct! Add 11x to both sides!!
Great Job!
-11x + 11y = 33 +11x +11x
11y = 33 + 11x 04/21/23 Geometry CP 30
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-4x + 2y = 8Correct! Add 4x to both sides!!
Great Job!
-4x + 2y = 8 +4x +4x
2y = 8 + 4x 04/21/23 Geometry CP 31
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-8x - 4y = -16Correct! Add 8x to both sides!!
Great Job!
-8x - 4y = -16 +8x +8x
-4y = -16 + 8x 04/21/23 Geometry CP 32
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7x + y = -2Correct! Subtract 7x from both sides!!
Great Job!
7x + y = -2 -7x -7x
y = -2 – 7x 04/21/23 Geometry CP 33
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2x + 2y = 10Correct! Subtract 2x from both sides!!
Great Job!
2x + 2y = 10 -2x -2x
2y = 10 – 2x 04/21/23 Geometry CP 34
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-5x + 3y = -9Correct! Add 5x to both sides!!
Great Job!
-5x + 3y = -9 +5x +5x
3y = -9 + 5x 04/21/23 Geometry CP 35
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-8x - 4y = 24Correct! Add 8x to both sides!!
Great Job!
-8x - 4y = 24 +8x +8x
-4y = 24 + 8x 04/21/23 Geometry CP 36
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6x – 12y = -36Correct! Subtract 6x from both sides!!
Great Job!
6x – 12y = -36 -6x -6x
-12y = -36 – 6x 04/21/23 Geometry CP 37
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-2x – 2y = -14Correct! Add 2x to both sides!!
Great Job!
-2x – 2y = -14 +2x +2x
-2y = -14 + 2x 04/21/23 Geometry CP 38
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GREAT GAME!!!!
Please go back to your seats, we are going to return to our notes and get this first step written down and committed to memory
04/21/23 Geometry CP 39
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First StepExample Problem 1
6x + 3y = 9
04/21/23 Geometry CP 40
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First StepExample Problem 2
-10x + 2y = 8
04/21/23 Geometry CP 41
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First StepExample Problem 3
x - 2y = 4
04/21/23 Geometry CP 42
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First StepExample Problem 4
-x + y = -2
04/21/23 Geometry CP 43
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First StepExample Problem 5
-8x – 2y = -2
04/21/23 Geometry CP 44
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Your Turn
• With your shoulder buddy, complete the 10 problems on the next page.
• Remember, you are only showing the first step!
• You have 5 minutes to get this completed
04/21/23 Geometry CP 45
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Pair Race Directions
Equations are going to flash on the screen. The first one to step forward and show the first AND second steps to converting the equation will win.
Circle the slope and square on y-intercept
What ever side of the room has the most points wins!
EVERYONE….Please pay attention
04/21/23 Geometry CP 46
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Example4x + 2y = 18
The first step is: Subtract 4x from both sides
That would look like:
4x + 2y = 18 -4x -4x
2y = 18 – 4xThe second step is: Divide everything by 2
2y = 18 – 4x2 2 2
Final Result: y = 9 – 2x04/21/23 Geometry CP 47
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Example-14x + 7y = 28
The first step is: Add 14x to both sides
That would look like:
-14x + 7y = 28 +14x +14x
7y = 28 + 14xThe second step is: Divide everything by 7
7y = 28 + 14x7 7 7
Final Result: y = 4 + 2x04/21/23 Geometry CP 48
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Example-8x – 2y = -10
The first step is: Add 8x to both sides
That would look like:
-8x – 2y = -10 +8x +8x
-2y = -10 + 8xThe second step is: Divide everything by -2
-2y = -10 + 8x
-2 -2 -2Final Result: y = 5 – 4x
04/21/23 Geometry CP 49
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Example12x – 6y = 18
The first step is: Subtract 12x from both sides
That would look like:
12x – 6y = 18 -12x -12x
-6y = 18 – 12x The second step is: Divide everything by -6
-6y = 18 – 12x-6 -6 -6
Final Result: y = -3 + 2x04/21/23 Geometry CP 50
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Let’s Race Again!
ReadySet
GO!!04/21/23 Geometry CP 51
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4x + 5y = 10First Step?
Correct! Subtract 4x from both sides!!
4x + 5y = 10 -4x -4x
5y = 10 – 4x Second Step?
Correct! Divide everything by 5!!04/21/23 Geometry CP 52
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04/21/23 Geometry CP 53
5y = 10 – 4x
y = 2 – 4/5x
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-6x + 3y = 12Correct! Add 6x to both sides!!
-6x + 3y = 12
+6x +6x 3y = 12 + 6x
Second Step?
Correct! Divide everything by 3!!04/21/23 Geometry CP 54
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04/21/23 Geometry CP 55
3y = 12 + 6x
y = 4 +2x
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9x - y = -8Correct! Subtract 9x from both sides!!
9x - y = -8 -9x -9x - y = -8 – 9x
What’s in front of the y…that is always there…we just don’t write it (because mathematicians are lazy )?
- 1y = -8 – 9x Second Step?
Correct! Divide everything by -1!!04/21/23 Geometry CP 56
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04/21/23 Geometry CP 57
-y = -8 – 9x
y = 8 +9x
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10x - 20y = 20Correct! Subtract 10x from both sides!!
10x - 20y = 20 -10x -10x -20y = 20 – 10x
Second Step?
Correct! Divide everything by -2004/21/23 Geometry CP 58
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04/21/23 Geometry CP 59
-20y = 20 – 10x
y = -1 +1/2x
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-11x + 11y = 33Correct! Add 11x to both sides!!
-11x + 11y = 33 +11x +11x 11y = 33 + 11x
Second Step?
Correct! Divide everything by 11
04/21/23 Geometry CP 60
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04/21/23 Geometry CP 61
11y = 33 + 11x
y = 3 +x
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-4x + 2y = 8Correct! Add 4x to both sides!!
-4x + 2y = 8 +4x +4x 2y = 8 + 4x
Second Step?
Correct! Divide everything by 2
04/21/23 Geometry CP 62
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04/21/23 Geometry CP 63
2y = 8 + 4x
y = 4 +2x
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-8x - 4y = -16Correct! Add 8x to both sides!!
-8x - 4y = -16 +8x +8x -4y = -16 + 8x
Second Step?
Correct! Divide everything by -4!!04/21/23 Geometry CP 64
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04/21/23 Geometry CP 65
-4y = -16 + 8x
y = 4 - 2x
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7x + y = -2Correct! Subtract 7x from both sides!!
7x + y = -2 -7x -7x
y = -2 – 7x Second Step?
Correct! There is no second step!
It’s already solved for y 04/21/23 Geometry CP 66
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04/21/23 Geometry CP 67
y = -2 - 7x
y = -2 -7x
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2x + 2y = 10Correct! Subtract 2x from both sides!!
2x + 2y = 10 -2x -2x 2y = 10 – 2x
Second Step?
Correct! Divide everything by 2!!04/21/23 Geometry CP 68
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04/21/23 Geometry CP 69
2y = 10 – 2x
y = 5 -x
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-5x + 3y = -9Correct! Add 5x to both sides!!
-5x + 3y = -9 +5x +5x
3y = -9 + 5x Second Step?
Correct! Divide everything by 304/21/23 Geometry CP 70
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04/21/23 Geometry CP 71
3y = -9 + 5x
y = -3 +5/3x
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-8x - 4y = 24Correct! Add 8x to both sides!!
-8x - 4y = 24 +8x +8x -4y = 24 + 8x
Second Step?
Correct! Divide everything by -404/21/23 Geometry CP 72
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04/21/23 Geometry CP 73
-4y = 24 + 8x
y = -6 - 2x
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6x – 12y = -36Correct! Subtract 6x from both sides!!
6x – 12y = -36 -6x -6x
-12y = -36 – 6x Second Step?
Correct! Divide everything by -1204/21/23 Geometry CP 74
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04/21/23 Geometry CP 75
-12y = -36 – 6x
y = 3 +1/2x
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-2x – 2y = -14Correct! Add 2x to both sides!!
-2x – 2y = -14 +2x +2x
-2y = -14 + 2x Second Step?
Correct! Divide everything by -204/21/23 Geometry CP 76
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04/21/23 Geometry CP 77
-2y = -14 + 2x
y = 7 - x
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Putting it all TogetherFirst & Second Step Example Problem 1
35x + 7y = 49
04/21/23 Geometry CP 78
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Putting it all TogetherFirst & Second Step Example Problem 2
-20x – 5y = -30
04/21/23 Geometry CP 79
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Putting it all TogetherFirst & Second Step Example Problem 3
-6x + 3y = 24
04/21/23 Geometry CP 80
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Putting it all TogetherFirst & Second Step Example Problem 4
-x + 2y = 4
04/21/23 Geometry CP 81
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Putting it all TogetherFirst & Second Step Example Problem 5
x + y = 8
04/21/23 Geometry CP 82
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Putting it all TogetherFirst & Second Step Example Problem 6
x + 4y = 8
04/21/23 Geometry CP 83
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Your Turn
• With your shoulder buddy, complete the 10 problems on the next page.
• Remember, you are completing the entire problem to solve for y.
• You have 10 minutes to get this completed
04/21/23 Geometry CP 84
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ERROR ANALYSISERROR ANALYSIS
JARED12x + 3y = 9 3y = 9 – 12x y = 3 – 4x
Ali12x + 3y = 9 4x + y = 3 y = -4x + 3
Four students rewrote the equation 12x + 3y = 9 into slope-intercept form. Determine who did it correctly. If the student did it incorrectly, explain the mistake.
Molly12x + 3y = 9 3y = 9 – 12x y = 3 – 12x
Mia12x + 3y = 9 3y = 9 – 12x y = 3 – 4x y = 4x - 304/21/23 Geometry CP 85
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JOURNAL TIME!!
What are the three power moves that get any standard form equation into slope- intercept form?
Write an example problem and rewrite it from standard form into slope-intercept form!
04/21/23 Geometry CP 86
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HOMEWORK!
Complete the Slope Intercept and Standard Form wsht
04/21/23 Geometry CP 87
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Pick a partner activity (10 mins)
• Pick a partner within your color group to work on the problem
• Make sure that you work TOGETHER and CHECK EACH OTHER’S WORK.
• This will be a graded assignment to earn bonus points on your quiz
04/21/23 Geometry CP 88
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You have 2 minutes to find your partner!
04/21/23 Geometry CP 89
Purple GroupColette
DanKaylaSydni
JonathanPhil
Pink GroupMeganTyheimTiyanaAlisa
Courtney
Orange GroupDaysiaTaylor
Chris MShielaAndy
Chris NAshleySteven
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Purple Group
Directions: • For the following problems
find the x & y intercepts. Show work!
• Don’t forget that the x intercept happens when y=0 and the y intercept happens when x=0
• Write all intercepts as an ordered pair (x,y)
Finding X & Y intercepts
a. 2x – 3y = 12
b. 2x + 3y = 12
c. 3x – y = 6
d. y – x = 5
04/21/23 Geometry CP 90
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Orange Group
Directions:
• Rewrite each equation into slope-intercept form (y =mx+b)
• Identify the slope and y-intercept
• Show all work!
Rewriting Equations
a) 3x + 2y = 28
b) 5y = 15 – 2x
c) 3y + 9 = 2x
04/21/23 Geometry CP 91
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Pink Group
Directions:• Rewrite each equation
into slope-intercept form (y =mx+b)
• Identify the slope and y-intercept
• Don’t forget the 3 POWER steps..Use your notes if needed!
• Show all work!
Rewriting Equations
a) x + y = 20
b) 5x + 4y = 24
c) 3x – 2y = 12
04/21/23 Geometry CP 92
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Solve Systems of Solve Systems of Equations by the Graphing Equations by the Graphing
MethodMethod
LLesson EEssential QQuestion:
Describe the types of solutions a system of equations can have?
04/21/23 94Geometry CP
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What is a system of What is a system of equations?equations?
A system of equations is when you have two or more equations using the same variables.
The solution to the system is the point that satisfies ALL of the equations. This point will be an ordered pair.
When graphing, you will encounter three possibilities.
04/21/23 95Geometry CP
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Intersecting Lines Intersecting Lines (One Solution)(One Solution)
The point where the lines intersect is your solution.
What is the solution?The solution of this graph is
(1, 2)
(1,2)
04/21/23 96Geometry CP
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Find the solution to the following Find the solution to the following system using the Graphing Methodsystem using the Graphing Method
y = -2x + 4
y = x - 2
Graph both equations. I will graph using slope-intercept form.
Graph the y-intercept, then the slope.
y = -2x + 4y –int. = (0, 4) and
Slope = -2/1 or 2/-1
y = x - 2y – int. = (0, -2) and Slope = 1/1 or -1/-1
04/21/23 97Geometry CP
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Step 2: Graph the Step 2: Graph the equations.equations.
y = -2x + 4
y = x - 2
Where do the lines intersect?(2, 0)
2x + y = 4
x – y = 2
04/21/23 98Geometry CP
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Step 3: Check your answer!Step 3: Check your answer!
To check your answer, plug the point back in for x and y into both equations and simplify.
y = -2x + 4 (0) = -2(2) + 40 = -4 + 40 = 0
y = -x + 2(0) = -(2) + 20 = 0
Nice job…let’s look how to solve it usingthe graphing calculator!
04/21/23 99Geometry CP
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Geometry CP 100
Quick Stop & Jot
DO ALL LINES ALWAYS HAVE A POINT OF INTERSECTION?
WHAT OTHER TYPES OF SOLUTIONS CAN SYSTEMS OF EQUATIONS HAVE?
04/21/23
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Geometry CP 101
Another type of solution
How would you describe these lines?
Y = 3x + 2
Y = 3x - 4
What do you think the solution, or point of intersection, is?04/21/23
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Parallel LinesParallel Lines(No Solution)(No Solution)
These lines never intersect! Since the lines never cross,
there is NO SOLUTIONNO SOLUTION!
Parallel lines have the same slope with different y-intercepts.
2Slope = = 2
1y-intercept = 2
y-intercept = -1
04/21/23 102Geometry CP
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Find the solution to the following Find the solution to the following system by the Graphing Methodsystem by the Graphing Method
y = 2x – 3
y = 2x + 1
Graph both equations using slope and y-intercept.
04/21/23 103Geometry CP
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Step 2: Graph the Step 2: Graph the equations.equations.
y = 2x – 3m = 2 and b = -3
y = 2x + 1m = 2 and b = 1
Where do the lines intersect?No solution!
Notice that the slopes are the same with different y-intercepts. If you recognize this early, you don’t
have to graph them!
04/21/23 104Geometry CP
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Step 3: Check your answer!Step 3: Check your answer!
Not a lot to check…Just make sure you set up your equations correctly.
I double-checked it and I did it right…
04/21/23 105Geometry CP
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Geometry Honors 106
Another type of solutionAnother type of solution
What do you notice about the graphs and equations?
y = -3x + 4
3x + y = 4
What do you think the solution, or point of intersection is?
04/21/23
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Infinitely Many SolutionsInfinitely Many Solutions
SAME LINE
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Coinciding Lines Coinciding Lines (Infinitely Many Solutions)(Infinitely Many Solutions)
These lines are the same! Since the lines are on top of
each other, there are INFINITELY MANY INFINITELY MANY SOLUTIONSSOLUTIONS!
Coinciding lines have the same slope and y-intercepts.
2Slope = = 2
1y-intercept = -1
04/21/23 108Geometry CP
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Geometry CP 109
Find the solution to the following Find the solution to the following system by the Graphing Methodsystem by the Graphing Method
Graph 6x + 4y = 12 and 3x + 2y = 6
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Geometry CP 110
JOURNAL: Does it have a solution?
1) 1)
Determine whether the following have one, none, or infinite Determine whether the following have one, none, or infinite solutions by looking at the solutions by looking at the slopeslope and and y-intercepty-intercept. . Explain your reasoning. Explain your reasoning.
y = 4 -1/2 xy = 4 -1/2 x
y = 2x + 4y = 2x + 4
3) 3) 2) 2) y = -3/4x + 6y = -3/4x + 6
y = -3/4x - 6y = -3/4x - 6
y = -6x + 8y = -6x + 8
y + 6x = 8y + 6x = 8
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Geometry CP 111
Does it have a solution?
1) 1)
Determine whether the following have one, none, or infinite Determine whether the following have one, none, or infinite solutions by just looking at the solutions by just looking at the slopeslope and and y-intercepts.y-intercepts.
3) 3) 2) 2)
ANS:ANS: One SolutionOne Solution
ANS:ANS: No SolutionNo Solution
ANS:ANS: Infinite SolutionsInfinite Solutions
04/21/23
y = -3/4x + 6y = -3/4x + 6
y = -3/4x - 6y = -3/4x - 6
y = -6x + 8y = -6x + 8
y + 6x = 8y + 6x = 8
y = 4 -1/2 xy = 4 -1/2 x
y = 2x + 4y = 2x + 4
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What is the solution of the What is the solution of the system graphed below?system graphed below?
1. (2, -2)
2. (-2, 2)
3. No solution
4. Infinitely many solutions
04/21/23 112Geometry CP
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What is the solution of this What is the solution of this system using the Graphing system using the Graphing
Method?Method?
y = 2x - 2y = 2x + 1
1. (2, -2)
2. (2, 1)
3. No solution
4. Infinitely many solutions
04/21/23 113Geometry CP
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What is the solution of this What is the solution of this system using the Graphing system using the Graphing
Method?Method?
y = 2x - 2y = 1/2x + 4
1. (4, 6)
2. (6, 4)
3. No solution
4. Infinitely many solutions
04/21/23 114Geometry CP
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What is the solution of this What is the solution of this system using the Graphing system using the Graphing
Method?Method?
y = 3x - 8y = 3x - 8
1. (3, 1)
2. (4, 4)
3. No solution
4. Infinitely many solutions
04/21/23 115Geometry CP
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What is the solution of this What is the solution of this system using the Graphing system using the Graphing
Method?Method?
y = 4x - 2-4x + y = -2
1. (4, -2)
2. (-2, 4)
3. No solution
4. Infinitely many solutions
04/21/23 116Geometry CP
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Solving a system of equations by Solving a system of equations by the the Graphing Method Graphing Method
Let's summarize! There are 3 steps to solving a system using a graph.
Step 1: Graph both equations.
Step 2: Do the graphs intersect?
Step 3: Check your solution.
Graph using slope and y – intercept. Be sure to use a ruler and graph paper!
This is the solution! LABEL the solution (x, y)!
Substitute the x and y values into both equations to verify the point is a solution to both equations.
04/21/23 117Geometry CP
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Summarize TimeSummarize Time
In your journals, write today’s date and the question below.
Describe systems of equations that have one solution, no solution, and infinitely many
solutions?
Include a graph and equations as examples.Answer the question in complete sentences
with lots of details.
04/21/23 Geometry CP 118
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Geometry CP 119
GRAPHING CALCULATOR
Rewrite equation in y = formUse the INTERSECT function to find the
intersection point
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04/21/23 Geometry CP 120
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Geometry CP 121
Your turn: GRAPHING EXAMPLES
y = - 3x and y = 2 – 4x
x + y = 1 and 2x + y = 4
3x + y = 1 and y = 8 +1/2x
2x + y = 1 and 5x + 4y = 10
y = 2x + 3 and y = -4 + 2x
6x + 4y = 12 and 3x + 2y = 6
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Geometry CP 122
GRAPHING CALCULATOR EXAMPLES
y = - 3x and y = 2 – 4x
x + y = 1 and 2x + y = 4
3x + y = 1 and y = 8 +1/2x
2x + y = 1 and 5x + 4y = 10
y = 2x + 3 and y = -4 + 2x
6x + 4y = 12 and 3x + 2y = 6
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(2, - 6)
(3, -2)
(-2, 7)
(-2, 5)
No solution
Infinitely Many
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““All I Do Is Solve” (Part I)All I Do Is Solve” (Part I)
http://www.youtube.com/watch?v=qxHCEwrpMw0&NR=1
04/21/23 123Geometry CP
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Check Your Check Your UnderstandingUnderstanding
Solve the system of equations using the Graphing Method. Check your solution.
y = 3x – 3
y = -x + 1
04/21/23 Geometry CP 124
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Group Self-Evaluation Group Self-Evaluation FormForm
Read each statement and rate your partner by circling one response for each statement.
04/21/23 Geometry CP 125
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Homework AssignmentHomework Assignment
Worksheet - Solve each system of equations by the Graphing Method.
04/21/23 Geometry CP 126