2D - 1 - OLD - day 3 - Review 2 - graphing ANS.notebook · 2D 1 OLD day 3 Review 2 graphing ANS.notebook 4 September 09, 2019 Review of Lines NO TECHNOLOGY Sketch each of the lines

2D 1 OLD day 3 Review 2 graphing ANS.notebook

1

September 09, 2019

Learning Goal

Ensure that we are comfortable with graphing linear relations

Review II.

Can you do these today?


2

September 09, 2019

Problems/Questions from the Homework?

?

Brainstorming!!

What words that you learned that are related to lines?

y=mx+b yintercept

extrapolate slope m

interpolate m= rise/run

perpendicularm=

parallel


3

September 09, 2019

What methods can you use to graph a straight line?

Table of Values choose numbers for x substitute x into the equation to find y find 35 points and graph

Intercepts to find the yintercept set x=0 solve for y

to find the xintercept set y=0 solve for x

plot the two intercepts and connect them

Slope and yintercept start at yintercept use rise and run to plot more points connect points


4

September 09, 2019

Review of Lines NO TECHNOLOGY

Sketch each of the lines without technology.

e) parallel to y=3x+6 and going through (2,4)f) perpendicular to y= 2x7 and going through (4,3)

y=mx+b


5

September 09, 2019


6

September 09, 2019

e) parallel to y=3x+6 and going through (2,4)


7

September 09, 2019

f) perpendicular to y= 2x7 and going through (4,3)

Homework

pg. 19 # 1hi, 2ce, 6cf

pg. 22 # 4fn, 5ab, 6ab

pg. 23 # 1ac, 2ace, 3bf, 4ace


8

September 09, 2019

Attachments

unit 1 numeracy.notebook

unit 2 powers.notebook

unit 3 polynomials.notebook

unit 5 equation of lines.notebook

unit 4 solving exam review.notebook

unit 6 slope.notebook

Unit 7, Getting Ready Notes.doc

Homework 0.1.1.doc

Homework 0.2.2.doc

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Jun 10-5:08 PM Unit 3:Polynomials monomialbinomialtrinomiallike termssimplifyexpandcollect2true

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Dec 13-3:02 AM True False x+x = x 2 1

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Dec 13-3:02 AM True False 3x - 3 = x 2

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Dec 13-3:02 AM True False 2k 2 - k is a binomial 3

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Dec 13-3:02 AM True False -6x + x = -5x 4

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Dec 13-3:02 AM True False 5(x-1) = 5x - 1 5

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Dec 13-3:02 AM 6 Which of the following show like terms? A 3x 2x -x 2 B 4a 4b 4c C 3y -y 8y D 3m 2 n 2mn 2 4mn

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Dec 13-3:02 AM 7 3x - 5 + 2x +3 can be simplified to: A 3x B x - 2 C 5x - 2 D 5x + 2

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Dec 13-3:02 AM 8 -3x(x+4) simplifies to: A -3x 2 + 4 B -3x -12 C -3x 2 +12x D -3x 2 -12x

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Dec 13-3:02 AM 9 What is the degree of 2u 3 v ? A 1 B 2 C 3 D 4

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Mar 19-7:45 AM Find a simplified expression for the perimeter of the triangle Type text herefalse 5n - 8 4n - 16 4n + 3

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Mar 19-7:45 AM Simplify (h + 5) - (3h -8) Type text herefalse

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Jun 11-2:42 PM












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Notes

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SMART Notebook


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Jun 11-3:24 PM slope 3 , y-intercept 4y=3x+4slope undefined , y-intercept 5y=5slope 4, yintercept 3y=4x+3y intercept 4 , x intercept -34x-3y=-12y=4x-3 and y=4x-8parallel linesy=4x-3 and y=-0.25x-6perpendiculare linesy=4x-3 and y=-4x-8neither parallel nor perpslope zero, no x-interceptx=5WordDescriptiontruefalsetruefalsetrue

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Mar 19-7:45 AM Finding the equation from a graph 1. find the ______________ 2. find the ______________ using m = ______________ 3. sub values into ______________ Type text herefalse Label y-intercept rise run y=mx+b slope

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Mar 19-7:45 AM Find the equation of the following line Type text herefalse

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Mar 19-7:45 AM Finding the equation from a point and a slope 1. sub the ___________ and the ___________ into ___________ 2. solve for ___________ 3. substitute the values of ___________ and ___________ into ___________ Type text herefalse Label y=mx+b y=mx+b slope b point b

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Mar 19-7:45 AM Find the equation of the line through the point (0,-5) with slope -2 Type text herefalse

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Mar 19-7:45 AM Finding the equation of the line given two points 1. find the _____________ using the formula m=y 2 -y 1 x 2 -x 1 2. find the value of _____________ 3. state _____________ using _____________ Type text herefalse Label _____ _____ equation y=mx+b slope y-intercept

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Mar 19-7:45 AM Find the equation of the line through the points (0,5) and (-4,-25) Type text herefalse

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Mar 19-7:45 AM Find the equation of the line through the points (1,5) and perpendicular to the line y=-2x+5 Type text herefalse

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Jun 11-3:29 PM


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flash/flash111/grade2Subject4.txt

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SMART Notebook



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Jan 14-12:24 PM resources/droppedImage.pngEnter text here.%# Use the pin to set the end position and click the arrow to go back to that location.definitiontrue58.999633789062558.9996337890625384111true30928

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Dec 13-3:02 AM 1 4x-2y-10=0 in slope y intercept form is A 2y=4x+10 B y=-2x-5 C y=2x-5 D y=-2x+5 resources/droppedImage.pngEnter text here. %#Use the pin to set the end position and click the arrow to go back to that location.what is this?true35.9985351562535.99853515625953911true478361

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Notes

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flash/flash/flash0.html

flash/flash/grade1Subject4.txt


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Notes

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SMART Notebook



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Jan 13-9:46 AM Slope

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Jun 10-5:36 PM the slope of a lineis the steepness of the line%#and can be positve, negativezero or undefined.undefinedtruefalsetrue

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Jun 10-5:39 PM truefalseundefinedpositve slopes move up and rightnegative slopes move down and lefthorizontal lines have m=0vertical lines have m=0slope 5 is more steep than slope 4two lines are perpendicular if there slopes are equalslope is the steepness of a lineslope is run over riserate of change is the sloperate of change must have a unitthe slope of a distance time graph is the speed010101010101010122falseundefinedtrue

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Jan 13-9:49 AM Slope from a graph

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Jan 13-9:49 AM What is the slope of this line?

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Jan 14-11:20 AM What is the slope of this line? 2 4 6 8 1 2 3 4 5 -2 0

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Jan 13-9:51 AM

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Jan 14-11:43 AM The y-intercept

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Jun 10-5:47 PM y -interceptfirst differencefixed costrate of changeCROCdirect variationoriginpartial variatioriserunx-intercepteqn of a linecartesian planeconstantvariable rate2true

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Jan 13-9:51 AM Graph the line with the following characteristics. a. slope -2 and y-intercept 6 b. slope 1 and y-intercept -4 3

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Jan 14-11:44 AM A B C D match the equation to each x = -7 y = -7 y=-x+3 y=0.5x -4

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Jan 13-9:53 AM For the following line state slope:__________ y-intercept:_______ equation:________

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Jan 14-11:55 AM Find the true statement For the line y=-2x+6 a. the slope is 2 and the y-intercept is 6 b. the slope is -2 and the y-intercept is -6 c. the slope is 6 and the y-intercept is -2 d. the slope is -6 and the y-intercept is -2 e. the slope is -2 and the y-intercept is 6

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Jan 14-11:57 AM Given the following data, determine the equation of the line

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Jan 13-9:53 AM

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Jun 10-5:32 PM


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Notes

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SMART Notebook

MPM 2D – NOTES – Unit 1

GETTING READY

A. Algebraic Expressions

EXPRESSION: Any number of terms that can be evaluated by substituting numbers in place of the variables.

Ex. 2x + 5 or 9(x + 1) – 3x + 2y(y + 3)

***Notice that there is NO equal sign***

TERM: The product between a coefficient (numerical) and a Variable (letter).

Ex. 5x, 2x, 3x2, 9xy, 4

x

*** 5x and 2x are like terms.

*** 2x and 3x2 are not like terms.

It looks like there is no variable beside 4. It is a term. It has a special name.

It is called a _______________ term.

In fact, there is a literal term beside the 4, that we don’t see.

Do you know what it is? __________

POLYNOMIALS

(many) terms

y

x

monomialbinomialtrinomial

( 1 term )( 2 terms )( 3 terms )

ex. 2xex. 2x + 3yex. 2x + 3y – 1

DISTRIBUTIVE PROPERTY: Multiplying the outside term with each term inside a bracket.

a(b + c) = ab + ac

B. EQUATIONS: Any mathematical sentence that states that 2 quantities are equal ( ie. L.S. = R.S. ).

Ex. 2x + 3y = 6

Can you think of a value for x and a value for y that would make the above statement true? Take an educated guess, then use proper format in the space provided to show your work.

*** The solution that made L.S. = R.S. is also known as a root of the equation. Can an equation have more than 1 root?

Explain. __________________________________________________________

__________________________________________________________

__________________________________________________________

*** Can an equation have NO roots?

Explain. __________________________________________________________

__________________________________________________________

__________________________________________________________

*** A linear equation is an equation that forms a straight line when graphed.

Do you remember how many points you need to graph a straight line? ________________________

Is it a good idea to use more points? WHY?

__________________________________________________________________

__________________________________________________________________

C. GRAPHING LINEAR EQUATIONS

1. Table of values: Substitute in numbers for x and y to make the statement true.

Ex. 2x + 3y = 6

Use this table to graph the equation on the grid below.

x

x y

-3 4 2(-3) + 3y = 6

-6 + 3y = 6

0 2 3y = 12

y = 4

3 0

2. Using intercepts: Where the graph of the line crosses the x and y- axis.

x – intercept, let y = 0

2x + 3y = 6

2x + 3(0) = 6

2x = 6

x = 6

y – intercept, let x = 0

2x + 3y = 6

2(0) + 3y = 6

3y = 6

y = 2

*** Look at the graph you made before. Does the line pass through

the x and y – axis at these points?

__________________

3. Using the slope (m) and y – intercept : we need to rearrange the equation into the form y = mx + b.

y = mx + b

slope y – int

2x + 3y = 6 ( rearrange the equation to y = mx + b form )

3y = -2x + 6

y = -2 x + 2 ( 3

3

slope y – int

*** m = rise up or down

run over

= -2

3

( down 2 , over 3

y

*** Try graphing the equation using this method. Does it look like the other graph?

___________

D. SLOPE AND THE EQUATION OF A LINE :

1. Given 2 points :

1

2

1

2

x

x

y

y

m

-

-

=

or

2

1

2

1

x

x

y

y

m

-

-

=

, make sure to use the same direction when calculating y values and x values.

Ex. Determine the slope of AB given A( 1, 3 ) and B( 2, -4 ) .

7

1

7

1

4

3

2

1

)

4

(

3

-

=

-

=

-

+

=

-

-

-

=

m

2.Determine the equation of the line with slope of 3 and passing through (-1, 5).

y = mx + b

5 = 3(-1) +b Sub in all known values and solve for b .

5 = -3 + b

8 = b

( y = 3x + 8 (Slope-Intercept form)

or 3x – y + 8 = 0 ( Standard form )

E. SOLVING SYSTEMS OF EQUATIONS: Point of Intersection:

Does the following pair of lines intersect at the given point?

y = 3x + 1 and y = 2x + 3 ; ( 1, 4 )

4 = 3(1) + 1 4 = 2(1) + 3

4 = 4 4 = 5

L.S. = R.S. L.S. ( R.S.

( They do not intersect at that point… The point must satisfy both equations.

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SMART Notebook

MPM 2D__

NAME : ________________________

DATE : _________________________

Part A

Place your responses in the space provided. Each answer is worth one mark.

1. Determine the slope of the line -2y = -3x + 1

_________________________

2. Give an example of a monomial

_________________________

3. What is the x-intercept of y = 3x + 2 ?

_________________________

4. Write (-1)6 x (-1)2 as a single power

_________________________

5. Simplify

y

_________________________

6. Evaluate 2-2 (no decimals)

_________________________

7. Factor -4a2b2 – 6ab2

_________________________

8. Give the equation of a line parallel to x = 3

_________________________

9. Find the value of the expression 3a2b2 if a = -4 and b=2

_________________________

10. Give the equation of a line perpendicular to y =

7

1

x + 3 _________________________

Part B

Place your responses in the space provided.

11. Determine the slope of the line segment connecting the points G(4, -7) and H(-5, -2).

xy

y

x

14

21

2

3

12a) Simplify 6(2t2 + 3t + 1) - 2(t2 + 4t - 5) b) Solve 2y – 7 = 3(y -5)

13. Does the point (1, -3) lie on the line 2x + y = 9? Show your work.

14. For the equation: 8x + 4y = 12

a) Express the above equation in the form

y = mx + b.

y

b) Use the slope and the y-intercept to graph the relation.


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