Chibi-Robo quietly waits on top of the desk for all of Linebeck's students to take a seat.
Telly-Vision flies down from above everyone's vision and flicks the lights off. Soon enough, a small mechanical noise is heard from the desk, and the white-board is suddenly illuminated as a presentation begins to play on it.
Hello, students
I will be substituting for instructor Linebeck today
At the end of this Citrusoft ForceDot Presentation
I will return your grades for Problem Set #2
For those of you that missed classes
I will offer an assignment that can be turned in
to make up your missing problem set
Today, we will go over Linear Equations
Basically, we are taking Algebra and Graphs
And putting them together
Any algebraic expression can be represented in a graph
But only a few basic formulas will result in straight lines
I am sure the instructor will cover formulas that result in
curves and more complex shapes later
Let us begin
General form
Ax + By + C = 0
Every graph that uses the above formula
(assuming, by convention, that A > 0)
represents a straight lines, and all straight lines can be
represented by this formula
If A is non-zero, then the x-intercept will be -C/A
The x-intercept is the x-coordinate where the graph crosses
the x-axis (y is zero)
If B is non-zero, then the y-intercept will be -C/B
The y-intercept is the y-coordinate where the graph crosses
the y-axis (x is zero)
Every line has a slope that determines what angle the graph
appears on the plane, and is represented by the letter m
Standard form
Ax - By = C
A, B, and C are integers whose
greatest common factor is 1, A and B are
not both equal to zero, and A is non-negative
This form can be converted to the General form
but not always to other forms
Slope-intercept form
y = mx + b
and
y - y = m(x - x1)
The formula on the top is the Y-axis formula
it is very simple, but requires that you know the value
of the slope before utilizing it
The formula below it is the Point-slope form
It is a separate form
but I will show you a handy trick that some of you
may already know
Using that form, we can obtain the slope from
any pair of points
First, we pick a point on the plane
let us say (1,1)
and we will let them serve as our x1 and y1
Now, let us try to solve the form for m
which I hope you recall is the slope's value
m = (y - y1)/(x - x1)
We now have a formula to obtain the slope
(When using the General formula
the slope's formula is as follows:
m = A/B
If B is nonzero, however, it is:
m = -A/B
Thus becoming an inverted slope)
Now, we can substitute x and y
with any number of points and find the slope
(and thus the linear equation)
between the first point, (1,1)
and any other point we can think of
I will use (3,5) as an example:
m = (5 - 1)/(3 - 1)
m = 4/2
m = 2
And now for the Point-slope form:
y - 1 = 2(x - 1)
and we want to solve for y:
y = 2(x - 1) + 1
Notice that if we substitute x with 3,
y will equal 5
This is a sign that our equation is correct
and we have obtained a graph that passes through
both points (1,1) and (3,5)
Assignments
1. What is the slope between points (2,4) and (5,3)?
2. Draw the graph for a linear equation that goes through (1,1) and (5,3)
3. Write your own example of a linear equation in General Form
Make-up assignment
B. After drawing the first two graphs, write down at what point they intersect, and at what point each passes through an axis
Alphabetically organized grades
Andonuts, Jeff: A -
Bulbasaur: A -
Caroso, Panther: Skipped
Combusken: Skipped
Doe, Ninten: Skipped
Dragmire, Ganondorf: F
Flora, Daisy: B+, A -
Goombario: A -
Goombella: A -
Guy: A -
Hoshino, Kirby: Skipped
Kaze, Link: A -
Lucas: A -
Mudkip: Skipped
Nimbus, Mallow: Skipped
Oak, Green: Skipped
Peasley: Skipped
Pit: A -
Prower, Miles: Skipped
R.O.B.: A, A
Rose, Amy: A -
Roy: Skipped
Tony: B+, A -
Totodile: Skipped
Students that have not shown up for class must
turn in their make-up assignments if they wish
to avoid an I (for incomplete) grade for
any missed homework
Ask me or Telly-Vision for assistance with your
assignments or the lecture
You may leave once you are done