MATH 101 Lecture #4 - Linear Equations

[plug-into-adv.livejournal.com]

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

Comments

[fabulous-beans.livejournal.com]

Ah my my my... classes make themselves so difficult to rememeber! I shall have to extend an apology to our teacher.

*takes as accurate notes as possible* My study time will not be a waste, haha!

[pkloveomega.livejournal.com]

*was totally staring at Jeff throughout the lecture and therefore not listening to a word of it*

...H-huh?
*Snaps out of it once grades are given out*
(Did... did he mix up my mark with somebody else's...?
I... got an A - ...?)
Dad... Dad's gonna be so happy...!

Wow, maybe math isn't so hard after all.
...
*stares down at empty notes sheet, then at assignment he does not comprehend in the slightest*
...N-never mind.

[plug-into-adv.livejournal.com]

*the presentation loops after a moment, giving the students another chance to write down notes on it*

[starved-sword.livejournal.com]

Yes! That's even better than last time!

*takes notes as the presentation plays, and gets straight to work on the problems*

[blondprodigy.livejournal.com]

At least I salvaged my grade. Ergh.

*Takes very condensed notes, since he pretty much knows this stuff already, and gets to work on the questions. Every so often he sneaks a glance over at Lucas though, ffff.*

[not-a-tadpole.livejournal.com]

Oh no! I forgot last time! Well... I'll just have to work really hard to make up for it this time!

*Stares at the notes... then at the questions...*

. . .

I wish Grandpa taught me math.

[terriaki-blues.livejournal.com]

Yikes, that's a lot of math, Chibi!

Uhh...If anyone needs any help, I'm Telly, Chibi's assistant. I'm not that good at math, but..I'll speak for Chibi, since he can't speak for himself.

[plug-into-adv.livejournal.com]

*spins his hands around, projector playing the presentation over again on the white board after a while for anyone that may have missed it*

[pkloveomega.livejournal.com]

Oh, thank goodness...
*actually attempts to pay some sort of attention this time and get some notes down*

O-okay... maybe now, I...
...um...
*stares at assignment, still at a complete loss*
...

[arcaneflames.livejournal.com]

I... Am not anywhere on that list. Does that mean I don't have to turn anything in? :'D _{Because I totally was NOT ditching the last few times. Really.}

... And I did... uh... try to do last week's assignment. If you need it. *turns it in*

*works on the problems, fails miserably*

[terriaki-blues.livejournal.com]

*flies over* Uhh...If this is your first time taking this class, then you aren't on the list. But you'll have "I"s until you complete all the past assignments. We'll...grade what you handed in, then~

[dreamofballet.livejournal.com]

*writes everything down with a rather blank look on his face; stares at what he wrote for a while, frowning*

Er... this may sound a bit... weird, but I've never actually done much math before. Should I just try my best and see what happens, or...?

Why did I pick this as the first class to show up at? D:

[terriaki-blues.livejournal.com]

You should just try your best, yes! If you're really stuck, you could go and consult the text books in the back. But you shouldn't be too worried. I'm sure Linebeck will be lenient with new students, though.

[dreamofballet.livejournal.com]

Okay! That's good~ I'll go look at the books and try to figure it out, then. Thank you!

[loudflowerpower.livejournal.com]

Alright! B+, A-, not bad at all! :D

Would it hurt for this class to present its lessons in an easier-to-understand format? I feel like I'm in college already. Not even Pionpi is this hard to understand...

*takes notes VERY carefully, and reads them to herself a couple of times before getting to work on the current and make-up assignments*

[rivalrazorleaf]

Oh, Chibi! Your uniform looks really nice~

*Is rather pleased with his grade. Diligently takes notes and sets to work, determined to get a full A because he's a little nerd*

[multibonk.livejournal.com]

Hey, I'm improving! Great! *takes a few notes, then gets to work; he's had some experience with graphing before*

[twotailedgenius.livejournal.com]

I apologize for falling behind! *turns in missed assignments* I had a lot on my mind lately, hehe...they're still real easy problems all the same, a nice refresher course for me.

[the-fight-is-on.livejournal.com]

....
O_O
Um...let's see...well first...yay! Another A-...

1. What is the slope between points (2,4) and (5,3)?
I don't get it, Mr. chibi. D8

2. Draw the graph for a linear equation that goes through (1,1) and (5,3)
Uhh...I dont have any paper! D8 Nooooo.

3. Write your own example of a linear equation in General Form
3a+4b+8=19?

[youresosweet.livejournal.com]

Yaaaaaaay! *Jumps for joy*