Algebra Period 3 ( Review)

We won't be covering Chapter 7-1 in class.
This is simple Pre-Algebra!
I have included a review below:

Graphing Ordered Pairs 7 -1

Review of x y Coordinate Plane Graphing from Pre-Algebra (ch 7-1 in your book)

Cartesian plane: Named after French mathematician Descartes.
plane: a two dimensional (across and up/down) flat surface that extends infinitely in all directions.

quadrant: 2 perpendicular lines called axes split the plane into 4 regions....quad means 4
quadrant names: begin in the top right (where you normally write your name!) and go counterclockwise in a big "C" (remember it for "C"oordinate)
They are named I, II, III, IV in Roman Numerals

The axes are NOT part of any quadrant. A point on the x-axis or the y-axis is not in a quadrant since it is on the boundary between quadrants.

coordinate - A coordinate is the position of a point in the Cartesian plane
coordinate = "co" means goes along with (COefficient, COworker, CO-president, CO-champions)

"ordinate" means in order

So coordinate means numbers that go along with each other in a certain order
The numbers are the x and y values and the order is that the x always comes first

Also called an ordered pair (x y "ordered" and they are a "pair" of numbers)
Ordered pairs are recognized by the use of ( x , y ) format

origin = (0, 0) the center of the graph (its beginning or origin)
When you count the coordinate' s position, you count from the origin.

x comes before y in the alphabet so the order is (x, y) ....
always go right or left first, then up or down

the x axis is the horizontal axis (goes across)
Remember that because the number line also is horizontal and you learn that first
(the pattern to remember is x is always first and the number line is before going up and down)

NOW LET'S GET TO WHAT YOU ACTUALLY DO!!!
1) Count your x value:
positive x, count right from origin (positive numbers are to the right of zero on number line)
negative x, count left from origin
2) Count your y value:
positive y value, count up from where your x value was (up is the positive direction)
negative y value, count down from where your x value was (down is the negative direction)

EXAMPLE:
(3, 5) Count 3 to the right from the origin, then 5 up
(3, -5) Still count 2 to the right, but now count 5 down
(-3, 5) Count 3 to the left from the origin, then count 5 up
(-3, -5) Again count 3 to the left, but now count 5 down

BUT WHAT HAPPENS WHEN
ONE OF THE VALUES IS ZERO?
If the y value is zero it means that you move right or left, but don't go up or down:
SO YOUR POINT WILL BE ON THE x AXIS........x axis is where y = 0
Example: (3, 0) is a point on the x axis, 3 places to the RIGHT
Example: (-3, 0) is a point on the x axis, 3 places to the LEFT

If the x value is zero it means that you don't move right or left, you just go up or down.
SO YOUR POINT WILL BE ON THE y AXIS...........y axis is where x = 0
Example: (0, 3) is a point on the y axis, 3 places UP
Example: (0, -3) is a point on the y axis, 3 places DOWN

Graphing Equations Section 7-2
How do you determine whether a given number is a solution?
Plug it in, plug it in, plug it in! Do this carefully. Use ( ) when you plug in a value for x and for y.

How do you find a solution to an equation yourself?
Plug in for x and find y!
You can use ANY number for x
Then plug in your number and find y

How can you graph a linear equation?
Make an x/y table of values and then graph the coordinates.
You only need 3 coordinates to make a good line!
(The 3rd coordinate serves as a "check" for the other two...in case you made a mistake!)
I always try x = zero and y = zero first because it's usually easy. Then pick another easy x value!
If this doesn't work well (you get a fraction as an answer and that's not easy to graph),
then try setting x equal to 1, then 2, then 3

Linear Equations Section 7-3
What do they look like ( and what is not a linear equation?)
The variable is to the 1 power - like x, or y, or a, or b
What is not a linear equation? the variable is not to the 1 power - like x2, x3, etc, or 1/x (x-1)

2 ways to graph:
1) 3 points using a table (like Ch 7-2)
EXAMPLE: 2x - 3y = -6
x y
0 2
3 4
-3 0

2) 2 points using the y and x intercepts (where the line intersects the y and x axis)
Standard form of a linear equation: Ax +By = C
A, B and C should not be fractions
A should be positive (y will be positive or negative)
We won't be using this form to look at the slope of the line!
This is a good format for finding the x and y intercepts!

If it's in standard form, this way works great if both the x and y coefficients are factors of the constant on the other side of the equal sign.

EXAMPLE: 2x - 3y = -6
If x = 0, y = 2
If y = 0, x = -3

Special linear equations:
Ones that are parallel to either the x or the y axis:
Lines parallel to the y axis are vertical lines:
They end up as the form x = with no y variable in the equation at all!
EXAMPLE: x = 4 ends up as a vertical line at x = 4
Still don't get this???
Pick of few points with the x value of 4:
(4, 0) (4, 2) (4, -3)
Graph those and join them in a line.
What do you get???
A vertical line!

Lines parallel to the x axis are horizontal lines:
They end up as the form y = with no x variable in the equation at all!
EXAMPLE: y = 4 ends up as a horizontal line at y = 4
Still don't get this???
Pick of few points with the y value of 4:
(0, 4) (2, 4) (-3, 4)
Graph those and join them in a line.
What do you get???
A horizontal line!