Finding gradient of slope involving angle

[Kurokari]

Homework Statement

Find the equations of both the straight lines that are inclined at an angle of 45 ° with straight line 2x + y - 3 = 0 and passing through the point (-1 , 4)

Homework Equations

tan θ = (m1 - m2)/(1+ m1m2)

The Attempt at a Solution

If I were to use the equation above, how would I know which is m1 and m2? Is there anyway to test it out or deduce which is m1 and which is m2?

 

[haruspex]

Swapping m1 and m2 in the formula is equivalent to negating theta. You are looking for lines that make angle theta to a given line, so that would be both plus and minus. Therefore it does not matter which way you assign m1 and m2.

 

[Kurokari]

Well what about if there is a negative and and a positive?

Say m1 = -1 and m2 = 2

If we followed the formula, I would get a tanθ,
However if I were to swap them, I would instead get a negative tanθ. Or does this matter?

 

[haruspex]

Well what about if there is a negative and and a positive?

Say m1 = -1 and m2 = 2

If we followed the formula, I would get a tanθ,
However if I were to swap them, I would instead get a negative tanθ. Or does this matter?

That just says the angle between the m1 and m2 lines is θ. Whether you consider that as plus or minus depends on which of the two lines you start from. In the present problem you are asked for two lines at angle 45 degrees to a given line, so you want both cases.