Question

Find the equation of straight line making angle 45 degree with x-axis and passing through intersection of lines x+y=1 and x-y=1.

Answer 1

Heya User,

--> Considering the 45° angle.. straight line either goes a 45° above the         x-axis or a 45° below the x-axis...

--> Considering both the facts, frame two equations -->
      y = x + c  || y = -x + c   { slopes being '1' and '-1' }

--> Find the point of intersection of 'x + y = 1' and 'x - y = 1' by solving the S.L.V. and we get the point as ( 1 , 0 )

--> Hence, put the value of x, y in the equation to determine the constant 'c' --> c = '-1' , '1'

--> y = x - 1 || and || y = -x + 1 
=> x - y = 1 || and || x + y = 1 <-- are themselves the two lines...

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However, one can see that :->
---> x + y = 1 => y = -x + 1 => slope = -1 
---> x - y = 1 => y = x - 1 => slope = +1 

And hence, these two are the required lines....

Answer 2

Answer:

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