Algebra Period 3 (Wednesday)

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 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!