Shayaan_Mustafa
  • Shayaan_Mustafa
x-ky=1 State the geometric property common tho this family of lines.
Mathematics
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SOLVED
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katieb
  • katieb
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Shayaan_Mustafa
  • Shayaan_Mustafa
Book says all lines will pass through the x-intercept = 1 But how?
anonymous
  • anonymous
this equation can be written like x=ky+1 i think you can recognize y=mx+b form, no? just the x and y are switched.
Shayaan_Mustafa
  • Shayaan_Mustafa
yes you are right. but how did you do this? If I didn't post "Book says all lines will pass through the x-intercept = 1 But how?" Can you now tell me the answer?

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anonymous
  • anonymous
you have a linear equation. Linear means, it represents a line. Every line has 2 properties that totaly define it: 1) slope, 2) place where it cross the y axis (or x axis) So that's it
anonymous
  • anonymous
in this case the crossing point is comun to all the family, but the slope can take any value ,k. So : same crossing point, but different slopes
Shayaan_Mustafa
  • Shayaan_Mustafa
as you said "place where it cross the y axis (or x axis)". right? if you want you can write the equation in the form of y. but you write it in the form of x. kinldy make me understand.
anonymous
  • anonymous
its more easy. x=1+ky and y= (1/k)x-1/k are anyway the same. If you answer that the commun property is that the crossing point of y axis is -1/k, is also perfectly correct.
Shayaan_Mustafa
  • Shayaan_Mustafa
in x=1+ky, 1 is fixed and varies. I got your point. But in y=(1/k)x-1, (-1/k) is fixed and (1/k) varies? right?
anonymous
  • anonymous
right
anonymous
  • anonymous
good observation
anonymous
  • anonymous
i mean bouth 1/k and -1/k varies, becouse of k
Shayaan_Mustafa
  • Shayaan_Mustafa
now 1 more thing. If (-1/k) is fixed and (1/k) varies then it means k varies therefore (1/k) varies. So if k varies then (-1/k) should vary, how can it be fixed bro?
anonymous
  • anonymous
look the previous answer
anonymous
  • anonymous
the commun thing would be that the y crossing point depends the same way on the slope of the line
Shayaan_Mustafa
  • Shayaan_Mustafa
yes that was i mean then we can't write the given equation in the form of y.
anonymous
  • anonymous
why not?
Shayaan_Mustafa
  • Shayaan_Mustafa
yeah. i got you. thnx bro.
Shayaan_Mustafa
  • Shayaan_Mustafa
i understand.
Shayaan_Mustafa
  • Shayaan_Mustafa
will kindly answer me another question?
anonymous
  • anonymous
sure, if i can, :)

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