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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 yintercept, write down another equation. c. given that the first line has identical x and yintercepts, 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 yintercept 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 pointslope 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 xintercept and yintercept are identical. If you're not convinced y=xc x+y=c x=yc. Letting y = 0, (so we have the xintercept) x=c. Which is also the yintercept. 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  
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: another straight line question Quote:
 

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