MATH 101 Lecture #4 - Linear Equations

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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