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March 13th, 2009, 05:55 PM  #1 
Member Joined: Feb 2009 Posts: 52 Thanks: 0  Algebra confusion , linear equation
So im doing point slope formulas and my book nails me with this question Find and equation for this line, write ansers in slopeintercept form. Through (1, 3) with slope 2 Y  3 = 2(x  (1) ) I highlighted the part that confuses me. Apparently the CORRECT next step is Y  3 = 2 (x + 1) however im getting Y  3 = 2x  1 Why is it that x  (1) = 1 when 3  (1) = 4 ? typically ive been handling variables as being a postive 1 in equations IE x(4) = 4 my instructor said something about double negatives becoming a positive but im just trying to understand why since this is not multiplication or division. 
March 13th, 2009, 06:05 PM  #2 
Newbie Joined: Mar 2009 Posts: 11 Thanks: 0  Re: Algebra confusion , linear equation
y  3 = 2(x  (1)) the next part is y  3 = 2(x+1) because it's like saying "the opposite of negative 1 is positive one. One trick that I learned is that if there is something like (x  (1)). you just take the negative after the x and put it perpendicular over the negative in front of the 1 to make it a positive sign 
March 13th, 2009, 06:33 PM  #3  
Member Joined: Feb 2008 Posts: 89 Thanks: 0  Re: Algebra confusion , linear equation Quote:
To your first question, 3  (1) is NOT= 4. 3  (1) = 2. Recall that to subtract a number, is to add its opposite; that is, ab = a+(b). So, 3  (1) is equivalent to adding the opposite of 1 to 3. I.e., 3  (1) = 3 + 1 = 2. Similarly, therefore, x  (1) = x + 1. Another way to view this is via the distributive property. To that end, 2(x  (1)) = 2*x  (2*1) = 2x  2 = 2(x+1). Regards, Rich B. rmath4u2@aol.com  
March 13th, 2009, 06:45 PM  #4 
Member Joined: Feb 2009 Posts: 52 Thanks: 0  Re: Algebra confusion , linear equation
Thanks to the first poster for that little visual trick and thanks nikko for pointing that out. so, technically we treat x or any variable as being zero? ( i know it seems obvious since a lot of the time we figure out and assign a value to a variable) but i had read somewhere (perhaps misread) in my algebra book that you can think of variables as being 1 or having a 1 next to them so when i am seeing X  (1) i am thinking 1  (1) = 2 
March 13th, 2009, 07:47 PM  #5  
Newbie Joined: Mar 2009 Posts: 11 Thanks: 0  Re: Algebra confusion , linear equation Quote:
how is that false?  
March 13th, 2009, 08:21 PM  #6  
Member Joined: Feb 2009 Posts: 52 Thanks: 0  Re: Algebra confusion , linear equation Quote:
wait what? a negative minus a negative will always be positive? now i am really confused.  
March 13th, 2009, 09:23 PM  #7  
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Algebra confusion , linear equation Quote:
In the following I'm going to use the letter y instead of the letter x, so that it doesn't look like a multiplication sign.  2(y  (1)) Taking minus one is the same as adding plus one. So it simplifies into:  2(y + 1) What happens if you don't simplify before multiplying? Then you do this: [color=red] 2[/color] (y [color=blue]–[/color] [color=green](1)[/color] ) = [color=red]( 2)[/color] y [color=blue]–[/color] [color=red](2)[/color] [color=green](1)[/color] There are three successive minus signs. "Minus times minus" is plus, so... minus times (minus times minus) = minus times plus = minus.  2 y  2 You said above that "this isn't multiplying." Yes it is! You're multiplying by ONE or MINUS ONE, so you don't see the multiplication, because it isn't normally written in. (y) = 1 ( 1 y) = (1*1) y = y  
March 14th, 2009, 04:03 AM  #8 
Senior Member Joined: Mar 2009 Posts: 318 Thanks: 0 
It sounds like you're having trouble with negative numbers and taking them "through" parentheses, so you might want to brush up on these topics. [color=white]. . . . .[/color]Google results for "negative numbers" [color=white]. . . . .[/color]Google results for "simplify parentheses" Pick a couple of lessons from each link, and study their worked examples. Then see if the steps for your posted exercise make a little more sense. 
March 15th, 2009, 08:09 AM  #9  
Global Moderator Joined: Dec 2006 Posts: 19,299 Thanks: 1688  Quote:
 
March 15th, 2009, 11:54 AM  #10  
Senior Member Joined: Mar 2009 Posts: 318 Thanks: 0  Quote:
 

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