Question

x-ky=1
State the geometric property common tho this family of lines.

Answer 1

Book says all lines will pass through the x-intercept = 1
But how?

Answer 2

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.

Answer 3

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?

Answer 4

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

Answer 5

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

Answer 6

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.

Answer 7

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.

Answer 8

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?

Answer 9

right

Answer 10

good observation

Answer 11

i mean bouth 1/k and -1/k varies, becouse of k

Answer 12

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?

Answer 13

look the previous answer

Answer 14

the commun thing would be that the y crossing point depends the same way on the slope of the line

Answer 15

yes that was i mean then we can't write the given equation in the form of y.

Answer 16

why not?

Answer 17

yeah. i got you.
thnx bro.

Answer 18

i understand.

Answer 19

will kindly answer me another question?

Answer 20

sure, if i can, :)