Square roots and the coordinate plane

36 Simplify square roots35 Multiply and simplify square roots34 Graph Ordered Pairs33 Graph a line from standard form32 Find slope from two points31 Graph lines from point and slope30 Find slopes from equations29 Graph lines, slope intercept form28 Graphing systems of equations

Riddle

Which of the following statements are true?

1.         Exactly one of these ten statements is false.2.         Exactly two of these ten statements are false.3.         Exactly three of these ten statements are false.4.         Exactly four of these ten statements are false.5.         Exactly five of these ten statements are false.6.         Exactly six of these ten statements are false.7.         Exactly seven of these ten statements are false.8.         Exactly eight of these ten statements are false.9.         Exactly nine of these ten statements are false.10. Exactly ten of these ten statements are false.

36a Simplify Square RootsPerfect squares

22 = 432 = 942 = 1652 = 2562 = 3672 = 4982 = 64

92 = 81102 = 100112 = 121122 = 144132 = 169

Ex1. 8 Ex2. 1008

Ex3. 723 Ex4. 196516256

...

636

525

416

39

24

RiddleMr. Gray charges $5.00 to cut a log into two pieces. How much would he charge to cut a log into four pieces?

35a Multiply and simplify square roots

Ex1. 26 Ex2. 9060

Ex3. 641805

49162536496481100121144169196225

Riddle

How far apart are the rails on railroad tracks?

4 ‘ 11 ¾”

How did we devise that measurement?

34a – Ordered pairs

Remember that ordered pairs describe a location in terms of Remember that ordered pairs describe a location in terms of x and y such that (x,y).x and y such that (x,y).

These are always in alphabetical order

Where is point A and M located? A (-3,4) M(1,2)

Also recall the quadrant values

II I

III IV

Riddle

Many people who are interested in American history and politics, and especially Republicans, never tire of pointing out that Woodrow Wilson, a Democrat, was a character of such dubious qualities that when he ran for the presidency, his own mother didn't vote for him. Although he did win, why couldn't he have counted on his own mother's vote?

33a – Graph a line from standard form

Recall standard form of a line.

ax+by=c

Graph x+y=3

x y0 0+y=33

0 x+0=33

Graph the points and connect the dots

-5 5

4

2

-2

-4

To graph this, let’s find the intercepts

33b – Graph a line from standard form

Graph 3x-y=6

x y0 (3)0-y=6-6

0 3x-0=62

Graph the points and connect the dots

-5 5

4

2

-2

-4

33c – Graph a line from standard form

Graph 3x-4y=-12

x y0 (3)0-4y=-123

0 3x-(4)0=-12-4

Graph the points and connect the dots

-5 5

4

2

-2

-4

RiddleIn 1969 Pan American Airlines accepted over 80,000 reservations for commercial flights, but failed to specify either the dates or times of the trips. Furthermore, to this day, they have not bothered to honor a single reservation. Ironically, they haven't received any formal complaints. Why not?

32a Find slopes from two points

Slope can be defined as m= or or

Ex1. Find the slope of a line passing through points A(-2,-5) and B(6,1)

Run

Rise

x

y

12

12

xx

yy

-5-1

-2-6= -6

-834

=

Ex2. Find the slope of a line passing through points A(-2,4) and B(6,-5)

4--5

-2-6= 9

-8

| -98

Riddle

Two girls are born of the same parents in Boston, but not at the same time, otherwise they'd be twins. One of them, however, is a citizen of the United States and the other is not. How could this be? And one did not give up her citizenship.

31a Graph line from slope & point

Recall slope is Rise over Run

Ex1. Graph the line that goes through the point (-3, – 2)

and has slope 4

1

-5 5

4

2

-2

-4

31b Graph line from slope & point

Ex2. Graph the line that goes through the point (-4,1)

and has slope 5

3

-5 5

4

2

-2

-4

31c Graph line from slope & point

Ex3. Graph the line that goes through the point (3,-1)

and has slope 5

4

-5 5

4

2

-2

-4

Riddle

A cowboy leaves on Sunday and returns on Sunday. He was only gone 5 days, how is this possible?

30a Find slopes from equations

Remember y=mx+b ?

What did the ‘m’ represent? Slope

What did the ‘b’ represent? y-intercept

What type of an equation was this? Slope-intercept

To find the slope from an equation:

Solve for ‘y’. ( Get y = )

Whatever is in front of the ‘x’ is the slope!

30b Find slopes from equations

Ex1. What is the slope of the line 6x+3y=54?

6x+3y=54

3y=-6x+54 Subtract 6x from both sides

y=-2x+18 Divide both sides by 3

Slope is -2

Ex2. What is the slope of the line y= x+64

1

Slope is 4

1

30c Find slopes from equations

Ex3. Find slope of y+4=3(x-2)

y+4=3x-6

y = 3x-10

The slope is 3

What is so unusual What is so unusual about this sentence:about this sentence:

Jackdaw loves my big Jackdaw loves my big sphinx of quartz.sphinx of quartz.Jackdaw is a bird similar to a crowJackdaw is a bird similar to a crow

Riddle

29a Graph lines, SI form

y=mx+b

Slope y-intercept

Graph by placing the point and then using slope for Rise over Run

Ex1. Graph y=1/4x+2

-5 5

4

2

-2

-4

29b Graph lines, SI form

Ex2. Graph y=-x+4

-5 5

4

2

-2

-4

Ex3. Graph f(x)=4x-3

Riddle

There is a new medical There is a new medical complex being built complex being built and Larry was hired to and Larry was hired to paint the numbers 1 to paint the numbers 1 to 100 on the doors. How 100 on the doors. How manymany times will Larry times will Larry paint the numeral nine?paint the numeral nine?

28a Graph systems of equations

-5 5

4

2

-2

-4

x+3y=-6 -x+2y=-6

3y=-x-6

y=-1/3x-2

2y=x-6

y=1/2x-3

28b Graph systems of equations

-5 5

4

2

-2

-4

x+y=2 2x-y=-5

y=-x+2 -y=-2x-5

y=2x+5

28c Graph systems of equations

-5 5

4

2

-2

-4

y=2x+2 -6x+3y=12

3y=6x+12

y=2x+4

28d Graph systems of equations

Test tomorrow on sections:Test tomorrow on sections:

75 Simplify square roots75 Simplify square roots74 Multiply and simplify square roots74 Multiply and simplify square roots73 Use square roots to solve equations73 Use square roots to solve equations72 Graph Ordered Pairs72 Graph Ordered Pairs71Graph a line from standard form71Graph a line from standard form70 Find slope from two points70 Find slope from two points69 Graph lines from point and slope69 Graph lines from point and slope68 Find slopes from equations68 Find slopes from equations67 Graph lines, slope intercept form67 Graph lines, slope intercept form66 Graphing systems of equations66 Graphing systems of equations