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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