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#1 2013-01-03 13:25:11

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

lines

Suppose you graphed every single point of the form

. For example, when have
, we have
and
so
  is on the graph. Explain why the graph is a line, and find an equation whose graph is this line.

Last edited by cooljackiec (2013-01-03 13:26:24)


I see you have graph paper.
You must be plotting something
lol

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#2 2013-01-03 15:11:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,035

Re: lines

Hi;

and find an equation whose graph is this line.

(2 t + 3, 3 - 3 t)

You can think of this as

x = 2 t + 3 and y = 3 - 3 t;

Solve for t in x = 2 t + 3

substitute in the second equation y = 3 - 3 t

That is the equation of the line and it also answers the first part of the question.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2013-01-04 12:05:53

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: lines

Find the sum of all values of  a such that the point (a,7)  is

  from the point (2,1).

Last edited by cooljackiec (2013-01-04 12:08:39)


I see you have graph paper.
You must be plotting something
lol

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#4 2013-01-04 12:39:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,035

Re: lines

Hi

That is the equation of the circle that represents all the points that are 3√(5) from (2,1)

You want the intersection of y = 7 with that circle.

x = -1 and x = 5, so a = -1 and 5. Add them up and get 4.

See the drawing below.

View Image: 2013-01-04_164105.gif

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#5 2013-01-04 13:51:33

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: lines

Thanks. Nice profile pic


I see you have graph paper.
You must be plotting something
lol

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#6 2013-01-04 13:53:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,035

Re: lines

Hi;

You are welcome, everything understandable?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#7 2013-01-05 05:40:22

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: lines

find all x where

. Interval notation?


I see you have graph paper.
You must be plotting something
lol

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#8 2013-01-05 07:03:25

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,287

Re: lines

Treat it like an equation except replace the = sign with a ≤ sign.

Interval notation is like (-∞,20]  for x ≤ 20 except this isn't the answer; I just made it up as an example.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#9 2013-01-07 12:20:17

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: lines

I don't get when to use ( and ]


I see you have graph paper.
You must be plotting something
lol

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#10 2013-01-07 19:55:14

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,287

Re: lines

hi cooljackiec

Use [ or ] when the end point is included.  Use ( or ) when the end point is not included.

eg.

2 <   x   < 3  ............................    (2,3)

2 ≤   x   < 3 ..............................    [2,3)

You cannot reach ∞ so that end point will never be included.

x > 5            ................................ (5,∞)

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#11 2013-01-08 12:59:36

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: lines

I have a large truck and my neighbor has four identical small trucks. My truck can carry at least 800 pounds more than each of her trucks, but no more than one-third what all four of her trucks combined can carry. Knowing only these facts, what is the largest number of pounds that I can be assured of being able to carry in my truck?


I see you have graph paper.
You must be plotting something
lol

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#12 2013-01-08 16:59:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,035

Re: lines

Hi;

I am probably not understanding the question but this is what I am getting.

There is no largest amount you can be assured of carrying. The smallest amount is that your truck can carry 3200 lbs while each of her trucks can carry 2400 lbs.

View Image: 2013-01-08_203938.gif

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#13 2013-01-09 16:33:00

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: lines

up:cool:dizzy:DYou are correct


I see you have graph paper.
You must be plotting something
lol

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#14 2013-01-09 16:47:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,035

Re: lines

Hi;

I think we need more conditions to get an upper bound on the amount your truck can carry.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#15 2013-01-10 13:07:34

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: lines

Anyways, i have a new problem:

1)Let line

be the graph of
. Line
  is perpendicular to line
  and passes through the point (10,10). If line
is the graph of the equation y =mx + b, then find m+b.


2) Find B-A if the graph of Ax + By = 7 passes through (2,1) and is parallel to the graph of 2x - 7y = 3

3)The "perpendicular bisector" of the line segment

is the line that passes through the midpoint of
  and is perpendicular to
.

The equation of the perpendicular bisector of the line segment joining the points (1,2) and (-5,12) is y=mx+b. Find m + b.


I see you have graph paper.
You must be plotting something
lol

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#16 2013-01-10 13:18:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,035

Re: lines

Hi;

1) The equation of the line is  -8x + 5y = -30 so can you get m and b from that?

2) The equation of the line is  2x - 7y = -3, can you get A - B from that?


3) The equation of the perpendicular bisector is -3x + 5y = 41, can you get m and b now?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#17 2013-01-10 13:37:09

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: lines

I am still unsure about 2) and 3)


I see you have graph paper.
You must be plotting something
lol

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#18 2013-01-10 13:38:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,035

Re: lines

Hi;

Let's start with 2), which part are you unsure about?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#19 2013-01-10 13:39:48

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: lines

I think 3) is wrong, could you express it in slope intercept?


I see you have graph paper.
You must be plotting something
lol

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#20 2013-01-10 13:45:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,035

Re: lines

Hi;

Yes, the copy and paste still had the earlier one in there I am sorry. Check 3) now .


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#21 2013-01-10 14:15:26

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: lines

never mind, i understand it


I see you have graph paper.
You must be plotting something
lol

Offline

#22 2013-01-10 14:17:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,035

Re: lines

Okay, but call out if you need help. Sorry for the typo.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#23 2013-01-13 00:36:53

vgauti
Member
Registered: 2013-01-13
Posts: 1

Re: lines

A line drawn through A(4,-1) parallel to the line 3x-4y+1=0. Find the coordinates of the two points on this line which are at a distance of 5 units from A.

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#24 2013-01-13 00:49:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,035

Re: lines

Hi;

Welcome to the forum. If you mean the second  line, the one parallel to 3x-4y+1=0 then the points are (8 , 2) and (0, -4).

The equation of the parallel line is

the equation of the circle with center at (4 , -1) is

Solve them both simultaneously:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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