My Math Forum another straight line question

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 August 9th, 2008, 09:23 AM #1 Member   Joined: Aug 2007 Posts: 39 Thanks: 0 another straight line question the equations of two striaght lines are: ax + by + c = 0 dx + ey + f = 0 a. given that the lines do not intersect, write down an equation connecting a, b, d and e. b. given that the lines have the same y-intercept, write down another equation. c. given that the first line has identical x- and y-intercepts, write down a third equation. i have the answers, but i seriously have no flippin idea how the book got there. a. ae = bd b. ce = bf c. a = b could someone please explain how to get to these answers please?
 August 9th, 2008, 11:09 AM #2 Senior Member   Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 Re: another straight line question a) Since the two lines don't intersect, it means the slope of the two lines is the same. I.e. a/b = d/e. Cross multiplying gives us ae=bd. b) They have the same y-intercept and have the same slope. This means they are the same line. This makes us want to say that c=f. But the line x+y+1=0 is the same as the line 2x+2y+2=0. We arrive again at the two equations having similar ratios. So b/c = e/f, or bf=ce (also, af=cd works) c)look at the equation in point-slope form: y=-ax/b -c/b Now if a =b, we have y=-x -c. Which says it has a slope of -1. This means that the x-intercept and y-intercept are identical. If you're not convinced y=-x-c x+y=-c x=-y-c. Letting y = 0, (so we have the x-intercept) x=-c. Which is also the y-intercept. If you need me to be more specific, let me know. Cheers, Cory
 August 9th, 2008, 11:15 AM #3 Member   Joined: Aug 2007 Posts: 39 Thanks: 0 Re: another straight line question wow thanks! your a real genius!
August 10th, 2008, 07:45 AM   #4
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Re: another straight line question

Quote:
 Originally Posted by Kiranpreet wow thanks! your a real genius!
I wish. I've just been doing this long enough...

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