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March 13th, 2009, 05:55 PM   #1
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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 slope-intercept 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.
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March 13th, 2009, 06:05 PM   #2
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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
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March 13th, 2009, 06:33 PM   #3
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Re: Algebra confusion , linear equation

Quote:
Originally Posted by roncarlston
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.
Greetings:

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, a-b = 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
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March 13th, 2009, 06:45 PM   #4
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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
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March 13th, 2009, 07:47 PM   #5
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Re: Algebra confusion , linear equation

Quote:
so when i am seeing X - (-1) i am thinking 1 - (-1) = 2
yup. the same thing as saying "x minus the opposite of negative one. a negative minus a negative will always be a positive

how is that false?
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March 13th, 2009, 08:21 PM   #6
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Re: Algebra confusion , linear equation

Quote:
Originally Posted by achmeineye
Quote:
so when i am seeing X - (-1) i am thinking 1 - (-1) = 2
yup. the same thing as saying "x minus the opposite of negative one. a negative minus a negative will always be a positive

wait what? a negative minus a negative will always be positive?


now i am really confused.
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March 13th, 2009, 09:23 PM   #7
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Re: Algebra confusion , linear equation

Quote:
wait what? a negative minus a negative will always be positive?
No. Please ignore that.

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
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March 14th, 2009, 04:03 AM   #8
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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.
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March 15th, 2009, 08:09 AM   #9
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Quote:
Originally Posted by roncarlston
. . . my instructor said something about double negatives becoming a positive, but I'm just trying to understand why, since this is not multiplication or division.
There's a version of the rule about double negative becoming positive that applies to subtraction; it says that p - (-q) becomes p + q.
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March 15th, 2009, 11:54 AM   #10
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Quote:
Originally Posted by skipjack
There's a version of the rule about double negative becoming positive that applies to subtraction; it says that p - (-q) becomes p + q.
But p - (-q) = p - 1(-q) = p + (-1)(-q), so it's kinda still multiplication....
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