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Geometry Pre-AP
Algebra REVIEW
Solving Equations/Inequalities
Graphing: Slope, writing equations for lines, graphing lines
**** TEST on the material covered on
these slides Friday August 23
Ex. 1
3  2x 10  8x
3  2x  8x 10
3  10x 10
10
10
7  10x
10 10
7
x
10
To SIMPLIFY use this
checklist.
• Any fractions?
– NO
• Any ( )
– NO
• Any like terms
– YES – Combine
them using Integer
rules.
• Now ISOLATE the
variable
• and SOLVE
OYO
3x  5  7 x  21
7x
7x
4x 5  21
5
5
4x  16
4
4
x 4
To SIMPLIFY use this
checklist.
• Any fractions?
– NO
• Any ( )
– NO
• Any like terms
– NO
• So ISOLATE the
variables. Get
them together on
the same side
• Now SOLVE
Ex.2
Ex. 3
(9) 5 (9)
First, multiply each term by the
common denominator!!
-2 and 8 have a denominator of
one, so just multiply (-2)(9) and
(8)(9).
9
(9)
y28
5y 18  72
18 18
5y  90
5
5
y  18
Ex. 4
First, multiply each term by the
common denominator!!
-2 and 4 have a denominator of
one, so just multiply (-2)(5) and
(4)(5).
(5) 3 (5) (5)
x2 4
5
3x 10  20
10 10
3x  30
3
3
x  10
Ex. 7
Getting rid of fractions
(11) (11)4 (11) (11)5 (11)7
2 x   5x  
11
11 11
22x 4 55x 5  7
22x  55x 4  5  7
33x 1  7
1 1
33x  8
33 33
8
x   33
•Multiply by the
LCD
•Group like terms
•Combine like
terms
•Use integer rules
•Now solve.
Not on the notes!
EX.3
 Any
Ex.
1 Fractions?
 NO
 Any Parentheses?
 YES - Then Distribute
 Any Like Terms?
 NO
 Then ISOLATE
 Now SOLVE
3( x  7)  14
3x 21  14
21 21
3x  35
3
3
35
x
3
OYO.

Any Fractions?
–

Any Parentheses?
–

YES - Then Distribute
Any Like Terms?
–

NO
YES - Combine
Now ISOLATE
1  5( x  3)  4  4 x
1  5x 15 4  4x
1  x11
11 11
12  x
If c = 10 Find f
5
c  ( f  32)
9
5
10  ( f  32)
9

  
Less Than
Greater Than
Fewer Than
More Than
Uses open
circle to graph.
Uses open
circle to graph.
Less Than or
Equal to
Greater Than or
Equal to
At Most
At Least
No More Than
No Less Than
Uses closed
circle to graph.
Uses closed circle
to graph.
2) 2r3r 17 2r2r 14
1r 17  14
17 17
r  31
<----|----|----|----|----|---->
29 30 31
32 33
If the variable is on the “LEFT” side,
you can shade in the direction the
Inequality symbol points.
10m  3  9m  5
9m
9m
1m   
 
m 
<----|----|----|----|----|---->
6
7
8
9
10
Which direction do we shade?
8 p  96
8
8
p  12
<----|----|----|----|----|---->
10
11
12
13
14
Which direction do we shade?
NOTE: In solving inequalities if
you divide or multiply both
sides by a negative , the
inequality symbol
REVERSES!!!!!!
5. Solve and graph:
EX.3
FIRST,
Solve
for x.
Divide
each
term
by 2.
8  2x  4
2 2
2
4 
x
 2
NOW,
graph it!!
<---|---|---|---|---|---|---|---|---|--->
-5 -4 -3 -2 -1 0
1
2
3
OYO.
6. SolveStart
andingraph:
the
9  3x 12  9
middle and
solve for x.
12
12 12
3  3x  21
Now
divide
each
term by
3.
3 3
3
1  x  7
<---|---|---|---|---|---|---|---|---|--->
0
1
2
3
4
5
6
7
8
9. Solve and graph:
EX.4
3m  m  4
m m
2m  4
2
2
m 2
OR
2m  m  6
m m
3m  6
3
3
m 2
OR
<---|---|---|---|---|---|---|---|---|--->
-3 -2 -1
0
1
2
3
4
5
PRE-AP GEOMETRY
Algebra Review
GRAPHING!!!!!!
Ordered Pairs will be
(-,+)
(0,0)
Ordered Pairs will be
(+,+)
Also called Horizontal
Axis
Ordered Pairs will be
(-,-)
Ordered Pairs will be
(+,-)
Also called Vertical Axis
WHAT IS SLOPE?
Take 45 seconds to write down
everything that you know
about slope.
Types of lines
Angles up Angles down
Slope is ______
Positive
Slope is ________
Negative
Horizontal
Slope is ______
Zero
Vertical
Slope is _____
Undefined
EX. 1
down 1
1

Slope 

right
3
3
B
Read line from left to right
Going up—positive
Going down--negative
A
up
Slope 
1
right 4
y2  y1
m
x2  x1
EX.2
(x1, y1) (x2, y2)
(0, 4) (1, 2)
Example 1
 Label your points
(x1, y1) (x2, y2)
m
24
10
2
m
1
 2
 Plug points into formula
 Simplify top and bottom,
then divide the two
numbers
 Calculator (y2 - y1) divide
(x2- x2) enter
OYO….
ExampleOYO 2
(x1, y1) (x2, y2)
(7, -4) (9, -1)
1  4
m
97
3
m
2
y2  y1
m
x2  x1
 Label your points
(x1, y1) (x2, y2)
 Plug points into formula
 Simplify top and bottom,
then divide the two
numbers
 Calculator (y2 - y1) divide
(x2- x2) enter
OYO…
3)
Example 3-4
(x1, y1) (x2, y2)
(10, 5) (3, 5)
m
5  5
3  10
0
m
7
0
y2  y1
m
x2  x1
(x1, y1) (x2, y2)
4) (-4, 2) (-4, 0)
0  2
m
4  4
2  undefined
m
0
0
m
2
0
All HORIZONTAL lines
Have a ZERO slope.
2  undefined
m
0
All
VERTICAL
lines have
NO SLOPE.
Example #1
y  3x  5
Example #1
(0,5)
y-int
3
m  3 
1
down
m
 right
OYO….
1
y  x 1
Example
8
#3
y-int (0, 1)
1
m
8
up
m
 right
Go back to y-intercept
and do the exact opposite
of the slope
Down
m
Left
Example #2
2y  8
Example #5
y4
y  0x  4
Y= #
y-int
(0, 4)
Slope
m0
Graph will touch y-axis
When slope is zero. You will
graph a horizontal line.
Horizontal—like the horizon
Example #3
2x + y = 8
2x  y  8
2x

2x
y  2 x  8


(0,8)
2
m
1
Solve each equation
for y (y by itself)
y = mx + b
Write the y-intercept
as a point
(0, b)
Write the slope as a
fraction ( if it is not
already a fraction)
y  2 x  8
Graph
#7
y intercept
= (0, 8)
Slope
2
m
1
 Down2
m
 right 1
Writing Equations of a line…given 2 pts
( x1 , y1 ) ( x2 , y2 )
Step 1
Step 2
Step 3
Find “m”
Find “b”
(y-intercept)
Plug “m” & “b”
into equation
y = mx + b
y2  y1
m
x2  x1
y = mx + b
(plug in an “x”,
“y” and “m”)
m = _____
Go to next column
b = ____
Go to next column
You have
your answer
( x1 , y1 )
( x2 , y2 )
EX.1 (1, 2) and (5, 6)
Step 1
Step 2
Find m
y2  y1
m
x2  x1
2
6
m
5 1
m 4
4
m 1
Remember, you need
an “m” and a “b”.
Step 3
Find b
Find equation
Plug in x,y, & m
Plug in m & b
y  mx  b
y  mx  b
2 1(1)  b
2  1b
1 1
1
1 x  __
y  __
1  b
y  x 1
( x1 , y1 )
( x2 , y2 )
OYO. (3, 8) and (-1, -12)
Step 1
Step 2
Find m
y2  y1
m
x2  x1
8
m
1  3
12
m  20
4
m5
Remember, you need
an “m” and a “b”.
Step 3
Find b
Find equation
Plug in x,y, & m
Plug in m & b
y  mx  b
8  5(3)  b
8  15  b
15 15
7  b
y  mx  b
5 x __7
y  __
y  5x  7
( x1 , y1 )
( x2 , y2 )
Remember, you need
OYO. (-2, 3) and (4, -2)
an “m” and a “b”.
Step 3
Step 1
Step 2
Find equation
Find b
Find m
Plug in m & b
y2  y1
Plug in x,y, & m
m
x2  x1
2  3
m
4  2
m  5
6
y  mx  b
3
(6)
3
5
6 (2)
10 (6)
6
b
b
 6b
18  10
10 10
8  6b
6
4
3
6
 b
(6)
y  mx  b
4
5
3
y  __
6 x  __
5
4
y
x
6
3
( x1 , y1 )
( x2 , y2 )
EX.2 ( 4 , -2) and ( 4, 8)
Step 1
Find m
y2  y1
m
x2  x1
m
8  2
4 4
10
m
0
Step 3
Step 2
Answer the
B) Vertical
following Questions: lines cross
A, B, & C
which axis?
A) What
kind of
lines have
slopes that
are
undefined?
C) What is your
“x” coordinate
from each pair?
( x1 , y1 )
( x2 , y2 )
OYO (-4,2 ) and (3,2 )
Step 1
Step 2
Answer the
Find m
y2  y1
following Questions:
m
A, B, & C
x2  x1
m
2 2
3  4
0
m
7
A) What kind of
lines have slopes
that are equal to
zero?
Step 3
B) Horizontal
lines cross
which axis?
What is your “y”
coordinate from
each pair?