anonymous
  • anonymous
please please please help me! :( find the equation of the line passing through (1/2, -2) whose x int is one half of its y int
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1343132016563:dw| slope m=-2 so y+2=-2(x-1/2) y=-2x-1
anonymous
  • anonymous
hi! how were you able to get the x and y intercepts? :)
anonymous
  • anonymous
the drawing is just an example of line that have this property that x-int is half of y-int. It doesn't go through the point (1/2, -2). It is just to visualize the problem and to notice that the slope of such a line is -2

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anonymous
  • anonymous
ohhh 'cause my problem is actually finding out how to get the equation of that line :( and please explain why the slope would be then -2? thank you
apoorvk
  • apoorvk
Okay let's do it through equations :) So, the intercept-form a straight line for x-intercept 'a', and y-intercept 'b', is: \[\large \frac x a + \frac y b =1\] Now since, the y-intercept in double that of the x-intercept, it will be safe to replace 'b' with '2a'. What do you think?
anonymous
  • anonymous
yes i tried that... i couldn't get a final answer, though :( i got stuck... x/a+y/2a=1 then i can't think of another equation because things seem to be missing like for the slope intercept form there's no slope. for the 2 point form there's no other point. for the point slope form, there's no slope... :(
anonymous
  • anonymous
oh wait i just had an idea!
apoorvk
  • apoorvk
You don't need any other equation! The line passes through (1/2, -2), and so you put in x=1/2 and y=-2 in the equation, and find out 'a'! - is that the idea that you just had? :P
anonymous
  • anonymous
exactly!! HAHAHAHA i can't believe that took me forever to figure out!! i kept on focusing on the "other equation"!! wait let me solve try to this... hahaha
apoorvk
  • apoorvk
Take your time! :)
anonymous
  • anonymous
my x int is (-3/2, 0) and my y int is (0, -3) so y=-2x-3 !!:) yaaay! thank you sooo much apoorvk!!
apoorvk
  • apoorvk
@dydlf - hey you seem to have made a slight bit of a calculating error. x-intercept should be '-1/2' actually - and so your equation will change as well. Check it out.
anonymous
  • anonymous
OH RIGHT!! HAHAHAHA careless me! thank you, apoorvk! my bad! thanks, thanks! so it's y=-2x-1 !!:)
apoorvk
  • apoorvk
No worries mate ;)

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