unit 2 inequality quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

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Unit 2 Inequality Quiz 2 ( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

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Page 1: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Unit 2 Inequality Quiz2( 3n + 7) > 5n

-3 (3x + 5) > -5 (2x – 2)

Page 2: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Writing Equations of a Line

Y = mX + b m = slope of lineb = y intercept/ starting point(X,Y) = coordinates

Steps 1. Plot 1st point on Y- intercept 2. Plot slope from 1st point3. connect points with ruler4. sign line at end

Graph y = 1/2 x -2

X Intercept =

Y Intercept =

Page 3: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Writing Equations of a Line

Y = mX + b m = slope of lineb = y intercept/ starting point(X,Y) = coordinates

Steps 1. Plot 1st point on Y- intercept 2. Plot slope from 1st point3. connect points with ruler4. sign line at end

Y = 2/1 X -3

Page 4: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

How do we find slope without using a   coordinate plane?

  Y2 - Y1

Slope= ______ ________

    X2 - X1

Page 5: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Finding equation of a line with given slope

and 1 point

Y = m x + bSlope = 2

(0,4)

Steps

1. Plug given points into equation.

2. Solve for b.

3. Write equation.

Slope = 1/2

(2,1)

1. Plug given points into equation.

2. Solve for b.

3. Write equation.

Page 6: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Graph 6y < 6 x -12 Using table of values.

X y

X Intercept =

Y Intercept =

Test Point (0,0) and Shade

Page 7: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Graph -3y > 1 x +9 Using table of values.

X y

X Intercept =

Y Intercept =

Test Point (0,0) and Shade

Page 8: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Graph y > 1/2 x -2 Using a table of values.

X y

X Intercept =

Y Intercept =

Graphing InequalitiesTranslate into equation1. Y = 1/2 x - 22. Fill in table of values3. Graph line4. Shade after testing point

Page 9: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Is the point (3,5) on the line 3x + 2y = 1

How could we solve??

Page 10: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Madeline spent 120 minutes working on an English essay. On Tuesday, she spent 20 minutes linger than on Monday, and on Wednesday, she spent rwice as long as she did on Tuesday. How many minutes did she spend working on the essay each day if she finished on Wednesday?

Page 11: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)
Page 12: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Given 2 points graph a linear equation

  Y2 - Y1

Slope = ______ ________

    X2 - X1

Steps:

1. Find Slope

2. Sub 1 point and slope into equation.

3. Solve for b

4. Rewrite equation in proper form.

5. Graph

(1, 3) (3,4)x y x y

m=

b=

Page 13: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Y= mx + b

Graph y = 1/2 x -2

Plot

x y

Graph 2y -6 = 4x

Plot

x y

Page 14: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Write in slope-intercept form.

x + y = 12 4x -3y = 0

m= m=b=  b=

Finding equation of a line with given slope and 1 point

Slope = 2 (0, 4)

Steps

1. Plug given points into equation.

2. Solve for b.

Page 15: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Given 2 points graph a linear equation

  Y2 - Y1

Slope = ______ ________

    X2 - X1

Steps:

1. Find Slope

2. Sub 1 point and slope into equation.

3. Solve for b

4. Rewrite equation in proper form.

5. Graph

(1, 3) (3,4)x y x y

m=

b=

Page 16: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Graph the Equation

y - 6 = 3( x - 4)

y + 1 = 2( x - 5)

Page 17: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)
Page 18: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Formal Definition of a Function A function relates each element of a set with exactly one element of another set(possibly the same set).

X Does Not Repeat

x y1 22 43 64 8

x y1 22 42 64 8

Domain = X Range=Y

Page 19: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Write coordinates of each point listed

AB C D E

A

B

C

D

E

Page 20: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

12

3 4

Quadrants

Page 21: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

State type of slope

1.

2.

3.

4.

1

2

3

4

Page 22: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

http://kutasoftware.com/FreeWorksheets/Alg1Worksheets/Slope%20From%20a%20Graph.pdf

Page 23: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Find slope of line passing through given points.

(-4,1) and (3,4)

Steps 1.Plot points2.Count rise over run

M= Rise   Run

Page 24: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Find slope of line passing through given points.

(1,1) and (3,-4)

Page 25: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

http://kutasoftware.com/FreeWorksheets/Alg1Worksheets/Slope%20From%20an%20Equation.pdf

Finding slope from an equation

Finding Slope from an Equation

y = − 5 /2 x − 5 y = −4x − 1

2x − y = 1 −2y − 10 + 2x = 0

Steps1. Put equation in proper Y= MX +B form 2. Identify slope  

B = Y intercept or Starting Point

M = Slope

Page 26: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Finding Slope without using a Graph

Y2 - Y1______

X2 - X1

M =

X,Y X,Y( 2 ,3 ) ( 4, 4)

Steps1. Substitute Coordinates  into slope formula.2. Solve for M. (slope)

X,Y  X,Y( -2 ,3 ) (4, -4)

X,Y  X,Y(-27,36) (14, -47)

http://kutasoftware.com/FreeWorksheets/Alg1Worksheets/Slope%20From%20Two%20Points.pdf

Page 27: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)
Page 28: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Graph the given line

Y= 2x - 3

X Y

Make table for given line

Page 29: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Determine if the given point is on the given line:

Y= 2X + 2 (1,4) X Y

Steps1. Put equation in Y=mx+b form2. Graph on coordinate plane3. Check points

or 1. Plug equation into calculator2. Check points on table

Or

1. Substitute Values of X and Y into equation2. Simplitfy Equation3. Are both sides equal?

Page 30: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Determine if the given point is on the given line:

x = -4Y + 9 (1,2) X Y

Steps1. Put equation in Y=mx+b form2. Graph on coordinate plane3. Check points

or

1. Plug equation into calculator2. Check points on table

Page 31: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Evaluate f(x)

Given f(x) = 3x-2 and g(x) = 1/2 x + 7, evaluate:

1. f (-3)

2. g (6)

Page 32: Unit 2 Inequality Quiz 2( 3n + 7) > 5n -3 (3x + 5) > -5 (2x – 2)

Bonus

24 X + 8 + 10X = -2 (4 + 7X)