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

Question

anonymous · Answer

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slope m=-2
so y+2=-2(x-1/2)
y=-2x-1

anonymous · Answer

hi! how were you able to get the x and y intercepts? :)

anonymous · Answer

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

anonymous · Answer

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 · Answer

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 · Answer

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 · Answer

oh wait i just had an idea!

apoorvk · Answer

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 · Answer

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 · Answer

Take your time! :)

anonymous · Answer

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 · Answer

@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 · Answer

OH RIGHT!! HAHAHAHA careless me! thank you, apoorvk! my bad! thanks, thanks! so it's y=-2x-1 !!:)

apoorvk · Answer

No worries mate ;)