I need to find a slope of a line given an angle and an equation of a line

Question

The question is as follows: Two lines make an angle of tan^-1(1/4) with the line t, where t : 2x+y=3. Write down the slope of the line t.

Please I'm stuck on how to approach the question.

Answer 1

HINT: Use the formula you were taught--the tangent of the angle between 2 lines. You are given the tangent of the angle and the slope of one of the lines!

Answer 2

Difference of two slopes can be written with $tan(x-y)$ property

$$ tan(x-y) = (tan(x) - tan(y))/( 1 + tan(x)tan(y)) $$ $$ |x-y| = 1/4 $$ $$ \pm1/4 = (-2 - u)/(1 - 2u) $$

Now solve for u.