# What is the equation of the line that meets x + 3y = 1 at (1, 0) and makes an angle of 45 degrees with it. We have to determine the equation of the line that meets x + 3y = 1 at (1, 0) and makes an angle of 45 degrees with it.

The slope of x + 3y = 1

=> y = (-1/3)x + 1

is -1/3.

Let the slope of the required...

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We have to determine the equation of the line that meets x + 3y = 1 at (1, 0) and makes an angle of 45 degrees with it.

The slope of x + 3y = 1

=> y = (-1/3)x + 1

is -1/3.

Let the slope of the required line be M.

As the angle between the required line and x + 3y = 1 is 45 degrees.

tan 45 = 1 = `(M + (1/3))/(1 - M*(1/3))`

=> `1 - M*(1/3) = M + (1/3)`

=> `(4/3)*M = (2/3)`

=> M = 1/2

The slope of the required line is 1/2 and it intersects x + 3y = 1 at (1, 0).

This gives the equation of the line as (y - 0)/(x - 1) = 1/2

=> 2y = x - 1

=> x - 2y - 1 = 0

The required line is x - 2y - 1= 0

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