cunazza wrote:harsh.champ wrote:cunazza wrote:harsh.champ wrote:ajith wrote:harsh.champ wrote:Is line l parallel to the y-axis?
(1) The equation of line l is x = 4.
(2) The points (4. 2) and (4, - 5) are on line l .
harsh.champ, i DO NOT understand what you mean when you say the following:
For statement(2)lets say the eqn. of line is y=mx +c
Now putting (4,2) we get 2 = 4m + c
Putting (4,-5) we get -5 = 4m + c
As we can see that this is only possible when slope"m" is infinity [that is the line is parallel to the y-axis]
Slope "m" is infinity?!
Well,slope "m" = infinity is just a way of saying that the line is parallel to the y-axis.
It simply denotes that tan(theta) = 90 degrees.
I hope this clears your doubt.It is just another representation of the statement.
I'm still not convinced about what you wrote.
You say:
For statement(2)lets say the eqn. of line is y=mx +c
(A) Now putting (4,2) we get 2 = 4m + c
(B) Putting (4,-5) we get -5 = 4m + c
now, from here - if we get rid of the constant - we get:
(A) => m = 2/4;
(B) => m = -5/4.
Where is the infinity?
Well,in the upper statement you have equated c=0 which is not the case.
Now, let me represent the equations in this form:-
(A)2-4m = c
(B)-5-4m = c
Thus,we get that 2-4m =-5-4m
which is only possible when m=infinity
So,the equation will become 2 - [4 x(infinity)] = -5 - [4 x (infinity)]
=>-(infinity) = -(infinity)
Alternatively,let the equatio be x = m'y + c
Putting (4,2) :- 4 = 2m' + c
Putting (4,-5) :- 4 = -5m' + c
which means 2m' = -5m'
This is only possible when m'=0
This is a corollary to the above equation where we got m = infinity
I hope it is clear now.
It takes time and effort to explain, so if my comment helped you please press Thanks button
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