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. [tex]\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't <b>anything</b> "figured out" until you add the "= 4/5" 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 "slope" 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 "slope" of a line? Do you know how $$tan(\theta)$$ is defined where $\theta$[/tex][itex]is an angle of right triangle? Without knowing those, you can'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't paying attention before? No wonder you didn'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't understand, DON'T stop "paying attention". Concentrate on it and look at every detail. There was nothing there that you hadn't seen before.[/itex]

 

[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 [tex] tan(\theta)$$. when it comes to sin, cos, tan, etc... I am lost. i had geom in high school, three years later i went from algebra 1 straight to algebra 2.$$[/tex]