My Math Forum 3 problems i need help with

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 September 18th, 2009, 07:44 PM #1 Newbie   Joined: Sep 2009 Posts: 23 Thanks: 0 3 problems i need help with are these lines perpendicular, parallel, the same, or neither (1.) y =2/3 x + 3 and y = -3x + 2 (2.) 2x + 5y = 1 and y = 5/2x +4 (3.) y = 4x + 2 y = -1/4x - 10 separate question, needs worked out (4.) f (x) = -x^2 -1
 September 18th, 2009, 08:01 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: 3 problems i need help with If two lines are parallel then their slopes are the same. If two lines are perpendicular then the slope of of one line is the negative reciprocal of the other. Do you see why? Experiment with graphing. If neither of these conditions are true, then the lines are neither parallel or perpendicular or if one of the lines has undefined slope then the line parallel to it also has undefined slope, and the line perpendicular to it has zero slope. E.g. x = 3 and x = 4 are parallel and x = 3 and y = 2 are perpendicular.
 September 18th, 2009, 08:24 PM #3 Newbie   Joined: Sep 2009 Posts: 23 Thanks: 0 Re: 3 problems i need help with thanks, wow are u & me the only people on here?
 September 18th, 2009, 08:27 PM #4 Newbie   Joined: Sep 2009 Posts: 23 Thanks: 0 Re: 3 problems i need help with is this correct? 1.perp 2.neither 3.perp
 September 18th, 2009, 08:34 PM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: 3 problems i need help with Number three is correct. Try the other two again.
 September 18th, 2009, 09:29 PM #6 Newbie   Joined: Sep 2009 Posts: 23 Thanks: 0 Re: 3 problems i need help with i'm still working on the other 2 but can u help with this one? using the point-slope form of the line: y - y_1 = m(x - x_1) to find the equation of the line passing through the points (5, -3) and (-1, 5)
 September 18th, 2009, 09:40 PM #7 Newbie   Joined: Sep 2009 Posts: 23 Thanks: 0 Re: 3 problems i need help with 1. is neither 2. same am i right now?
 September 19th, 2009, 01:02 AM #8 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 By definition, two linear lines are said to be parallel to each other, if they do not intersect or meet, so parallel and being coincident (i.e. the same) are not the same meaning. So, the terms perpendicular, parallel and coincident differ from each other, therefore the word neither is incorrectly used in the problem, by means of English language. Let there be two linear equations as follows: $a_1x\,+\,b_1y\,+\,c_1\,=\,0$ and $a_2x\,+\,b_2y\,+\,c_2\,=\,0,$ where $a_1,\,a_2,\,b_1,\,b_2,\,c_1$ and $c_2$ are real numbers and $b_1\,\neq\,0,\,b_2\,\neq\,0.$ In the Cartesian coordinate plane, if the two given linear equations I've given are perpendicular to each other, then $0\,=\,a_1a_2\,+\,b_1b_2;$ if parallel to each other, then $0\,=\,a_1b_2\,-\,a_2b_1$ and $0\,\neq\,b_1c_2\,-\,b_2c_1;$ if coincident, then $0\,=\,a_1b_2\,-\,a_2b_1$ and $0\,=\,b_1c_2\,-\,b_2c_1.$ For this case and if necessary, convert a specific linear equation into the form $0\,=\,ax\,+\,by\,+\,c,$ where $a,\,b$ and $c$ are real numbers. There can be other possible explanations which could be seem more simple than this, but this is one of the correct methods to solve for the problems (1.), (2.) and (3.). (1.) Not perpendicular, parallel, nor the same. (2.) Perpendicular. (3.) Perpendicular.

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