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August 9th, 2008, 09:23 AM   #1
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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?
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August 9th, 2008, 11:09 AM   #2
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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
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August 9th, 2008, 11:15 AM   #3
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Re: another straight line question

wow thanks! your a real genius!
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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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