Graphing Inequalities Day8

8/8/2019 Graphing Inequalities Day8

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Solving Systems of

Equations

Graphing Linear Inequalities


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Objectives How dowe graph an inequality

Define a boundary line

Graphing a boundary line

Define the solution for a system ofinequalities

Find the s

oluti

on

of a system

of inequalities


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What isthe solution of an

inequality

Solution of an inequality are all the

ordered pairs (points) that make theinequality true.


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Graphing InequalitiesConsider the inequality

y x

66

44

22

22

11 4433 6655

11

33

55

y = x Graph

Boundary line

REMEMBER: Solution are allthe ordered pairs (points) thatmake the inequality true.


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y x

66

44

22

22

11 4433 6655

11

33

55

1. Pick two points from eachside of the graph

(4,1)

(1,3)


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y x

66

44

22

22

11 4433 6655

11

33

55

(4,1)

(1,3)

2. Check points if they makeinequality true.

(1,3) y xsubstitute into


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y x

66

44

22

22

11 4433 6655

11

33

55

(4,1)

(1,3)



3 1


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y x

66

44

22

22

11 4433 6655

11

33

55

(4,1)

(1,3)



3 1


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y x

66

44

22

22

11 4433 6655

11

33

55

(4,1)

(1,3)




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y x

66

44

22

22

11 4433 6655

11

33

55

(4,1)

(1,3)



1 4


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y x

66

44

22

22

11 4433 6655

11

33

55

(4,1)

(1,3)



1 4 X

X


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y x

66

44

22

22

11 4433 6655

11

33

55

(4,1)

(1,3)

3. Shade the side where the correctpoint lies.

X


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y x

66

44

22

22

11 4433 6655

11

33

55

(1,3)

3. Shade the side where the correctpoint lies.


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x - 2y 4

33

11

22--11 11 4433 6655

--22

22

x - 2y = 4 Graph

y = x - 212


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x - 2y 4

33

11

22--11 11 4433 6655

--22

22

x - 2y = 4 Graph

TEST POINTS !!

(0,1)

(6,0)

y = x - 212


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x - 2y 4

33

11

22--11 11 4433 6655

--22

22

(0,1)

(6,0)

(0,1)substitute into

x - 2y 4


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x - 2y 4

33

11

22--11 11 4433 6655

--22

22

(0,1)

(6,0)


x - 2y 4

0 - 2(1) 4

-2 4


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x - 2y 4

33

11

22--11 11 4433 6655

--22

22

(0,1)

(6,0)


x - 2y 4


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x - 2y 4

33

11

22--11 11 4433 6655

--22

22

(0,1)

(6,0)


x - 2y 4

6 - 2(0) 4

6 4 X

X


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x - 2y 4

33

11

22--11 11 4433 6655

--22

22

(0,1)

(6,0)

X

SHADE CORRECT REGION !!


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Examples

66

44

22

22

11 4433 6655

11

33

55

3y - 2x 91.

y = x + 32

3 GRAPH


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Examples

66

44

22

22

11 4433 6655

11

33

55

3y - 2x 91.

y = x + 32

3 GRAPH

TEST!!

(0,5)(0,5)

(3,0)

X

3(5) - 2(0) 9

15 - 0 9


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Examples2.

x - 3y > -3

y = x + 11

3

66

44

22

22

11 4433 6655

11

33

55

Graph

TEST!!

(0,5) (0,5)

0 - 3(5) > -3

0 - 15 > -3

X

X


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Solving a system of

Inequalities

Consider the system

x + y -1-2x + y < 2

33

11

22

--11

11 33

22

--22--33 --11


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Solving a system of

Inequalities

Consider the system

x + y -1-2x + y < 2

33

11

22

--11

11 33

22

--22--33 --11

TEST: (0,0)

Graph

0 + 0 -10 -1

(0,0)

y = - x - 1


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Solving a system of

Inequalities

Consider the system

x + y -1-2x + y < 2

33

11

22

--11

11 33

22

--22--33 --11

Graph

TEST: (0,0)-2(0) + 0 < 2

0 < 2

y = 2x + 2

(0,0)


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33

11

22

--11

11 33

22

--22--33 --11

33

11

22

--11

11 33

22

--22--33 --11

x + y -1 -2x + y < 2


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Solving a system of

Inequalities

Consider the system

x + y -1-2x + y < 2 33

11

22

--11

11 33

22

--22--33 --11

SOLUTION:

Lies where the two shadedregions intersect eachother.


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Solving a system of

Inequalities

Consider the system

-2x + 3y < -65x + 4y < 12

--11

33

11

22

--22

Graph

y = x - 223

3322 44--11--22 11TEST: (0,0)(0,0)

-2(0) + 3(0) < -6

0 < -6 X

X


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Solving a system of

Inequalities

Consider the system

-2x + 3y < -65x + 4y < 12

--11

33

11

22

--22

Graph

y = - x + 354

3322 44--11--22 11TEST: (0,0)5(0) + 4(0) < 12

0 < 12

(0,0)


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Solving a system of

Inequalities

Consider the system

-2x + 3y < -65x + 4y < 12

--11

33

11

22

--22

Graph

3322 44--11--22 11

(0,0) SOLUTION:

Lies where the two shadedregions intersect eachother.


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Solving a system of

Inequalities

Consider the system

-2x + 3y < -65x + 4y < 12

--11

33

11

22

--22

Graph

3322 44--11--22 11

(0,0) NOTE:

All order pairs in darkregion are true in bothinequalities.


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Solving a system of

Inequalities

Consider the system

x - 4y 124y + x 12

(0,0)

101088 1212664422

--22

66

22

44

--44

--66

TEST: (0,0)

(0) - 4(0) 120 - 0 12

0 12

Graph


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Solving a system of

Inequalities

Consider the system

x - 4y 124y + x 12

(0,0)

101088 1212664422

--22

66

22

44

--44

--66

TEST: (0,0)

4(0) + (0) 120 12

Graph


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HOMEWORK

Finish pg. 289 #8-16(solve the system ofinequalities by graphing)

#19 and 20.


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Problem ModelPatricios family, on average, drives their SUV more thantwice as many miles as they drive their car. His familys caremits 0.75 pounds ofCO2 per mile and the SUV emits 1.25

pounds ofCO2 per mile. Patricio is concern with theenvironment and convinces his family to limit the total CO2emissions to less than 600 pounds per month. How manymiles can they drive their car and SUV to meet this limit?

x

y

= SUV miles

= Car miles> 2yx

0.75y 1.25x 600


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Problem Model> 2yx

0.75y 1.25y 600


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Problem ModelThe science club can spend at most $400 on a field trip to adinosaur exhibit. It has enough chaperones to allow at most100 students to go on the trip. The exhibit costs $3.00 for

students 12 and under and $6.00 for students 12 and over.How many students 12 years and under can go if 20students over 12 go?

x

y

= Students 12 and under

= Students 12 and over4y3x 400+

yx 100+


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Problem Model

4y3x 400+

yx 100+


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Now you try

x

y

= front-page ads

= inside-page ads1y2x 30+

yx 20+

The Math Club want to advertise their fundraiser eachweek in the school paper. They know that a front-page ad

is more effective than an ad inside the paper. They havea total of $30 budget for advertising. It costs $2 for eachfront-page ad and $1 for each inside-page ad. If the clubwants to advertise at least 20 times, what are the differentpossibilities for the number of front-page and inside-page

ads.


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Now you try

1y2x 30+

yx 20+

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Graphing Inequalities Day8