Solve for Linear Function: Algebra 2 Help | Homework Statement

[offtheleft]

Homework Statement

having a little bit of trouble. some of the information is new to me. ill point out because I am copying this down from my notes.

let A & B define some linear function, y=f(x).
A = (1, 2), B = (6, 6)
C = (x, y), D = (x, y)

let (x, y) represent some arbitrary points on the line defined by f but, not on points A or B.

C is between A and B and, D is somewhere past B.

so far, i know what's goin on. i have the slope which is \frac{4}{5}.

here's where I'm lost, i might have zoned out because of my ADHD but this is what's going on

1, from A \rightarrow C, \frac{y-2}{x-1}

2, from B \rightarrow D, \frac{y-6}{x-6}

3, from B \rightarrow C, \frac{-(6-y)}{-(6-x)}

4, and from A \rightarrow D is the same as A \rightarrow C


I have no idea how all that was figured out ( from 1 - 4 ) someone please explain that to me?

and it continues into the next part

\frac{y-2}{x-1} = \frac{y-6}{x-6}

i can comprehend that.

(x-1)(x-6) \frac{y-2}{x-1} = (x-1)(x-6) \frac{y-6}{x-6}

not sure how that all happened.

than it goes too..

\frac{x-1}{x-1} [(x-6)(y-2)] = \frac{x-6}{x-6} [(x-1)(y-6)]

(this is where i started paying attention again)
cancel stuff out and do some fun algebraic gymnastics and i came up with this;

xy-2x-6y+12=xy-6x-y+6

more fun algebra stuff and i came up with;

y=\frac{4}{5}x+\frac{6}{5}







i have no problem doing certain things. but that whole middle piece just lost me until it ws put into some fun polynomial expression. i need to know how i got that

 

[HallsofIvy]

Homework Statement

having a little bit of trouble. some of the information is new to me. ill point out because I am copying this down from my notes.

let A & B define some linear function, y=f(x).
A = (1, 2), B = (6, 6)
C = (x, y), D = (x, y)

let (x, y) represent some arbitrary points on the line defined by f but, not on points A or B.

C is between A and B and, D is somewhere past B.

so far, i know what's goin on. i have the slope which is \frac{4}{5}.

here's where I'm lost, i might have zoned out because of my ADHD but this is what's going on

1, from A \rightarrow C, \frac{y-2}{x-1}

2, from B \rightarrow D, \frac{y-6}{x-6}

3, from B \rightarrow C, \frac{-(6-y)}{-(6-x)}

Yes, and each of those is equal to 4/5. you don't really need the "-" in (3) because -1/-1= 1. \frac{6- y}{6- x}[/itex] is sufficent. Of course that is exactly the same as \frac{y- 6}{x- 6}.<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> 4, and from A \rightarrow D is the same as A \rightarrow C </div> </div> </blockquote> Well yes, because C= D= (x,y)!<br /> <br /> <br /> [/quote]I have no idea how all that was figured out ( from 1 - 4 ) someone please explain that to me?[/quote]<br /> There wasn&#039;t <b>anything</b> &quot;figured out&quot; until you add the &quot;= 4/5&quot; part! What you wrote in 1- 4 is just \frac{y_1- y_0}{x_1- x_0} for two points (x_0, y_0) and (x_1, y_1). Those are all from the definition of &quot;slope&quot; of a line which you had already figured out was 4/5.<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> and it continues into the next part<br /> <br /> \frac{y-2}{x-1} = \frac{y-6}{x-6}<br /> <br /> i can comprehend that. </div> </div> </blockquote> Do you know the definition of &quot;slope&quot; of a line? Do you know how tan(\theta) is defined where \thetais an angle of right triangle? Without knowing those, you can&#039;t comprehend it. <br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> (x-1)(x-6) \frac{y-2}{x-1} = (x-1)(x-6) \frac{y-6}{x-6}<br /> <br /> not sure how that all happened. </div> </div> </blockquote> You are clearing the fractions by multiplying both sides by the denominators of the fractions.<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> than it goes too..<br /> <br /> \frac{x-1}{x-1} [(x-6)(y-2)] = \frac{x-6}{x-6} [(x-1)(y-6)] </div> </div> </blockquote> Okay, just to make it clear what is happening they move the corresponding numerator and denominator together so you can see they cancel. That was what I said before: they are clearing the fractions by multiplying by the denominators so the denominators cancel.<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> (this is where i started paying attention again) </div> </div> </blockquote> So you weren&#039;t paying attention before? No wonder you didn&#039;t understand!<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> cancel stuff out and do some fun algebraic gymnastics and i came up with this;<br /> <br /> xy-2x-6y+12=xy-6x-y+6<br /> <br /> more fun algebra stuff and i came up with;<br /> <br /> y=\frac{4}{5}x+\frac{6}{5}<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> i have no problem doing certain things. but that whole middle piece just lost me until it ws put into some fun polynomial expression. i need to know how i got that </div> </div> </blockquote> Sometimes you can do mathematics by memorizing formulas. Sometimes you actually have to <b>think</b>. If you get to a part you don&#039;t understand, DON&#039;T stop &quot;paying attention&quot;. Concentrate on it and look at every detail. There was nothing there that you hadn&#039;t seen before.

 

[offtheleft]

i didnt mean to stop paying attention. i have REALLY bad ADHD.

so that whole section where i had 1 - 4 was just a more complicated or elaborate way to find the slope?

after you clarified a few things i understand it more except for the <br /> tan(\theta). when it comes to sin, cos, tan, etc... I am lost. i had geom in high school, three years later i went from algebra 1 straight to algebra 2.