Final answer:
To find the slopes (m1 and m2) of the two lines, where one slope is double the other, one can use the formula involving the tangent of the angle between them. By solving the resulting equation using algebraic methods, the slopes of the lines can be determined.
Step-by-step explanation:
The question pertains to finding the slopes of two lines when given that one slope is double the other and the tangent of the angle between them is 1/3. Considering the slopes of the lines to be m1 and m2, with m2 = 2m1, we can use the formula tan(theta) = |(m2 - m1) / (1 + m1*m2)|, where theta is the angle between the two lines, to find the slopes.
Given that tan(theta) = 1/3, we substitute m2 = 2m1 into the formula, which gives us the equation 1/3 = |(2m1 - m1) / (1 + 2m1*m1)|. Simplifying this, we get 1/3 = |m1 / (1 + 2m1^2)|. This equation can now be solved for m1, and once we find m1, we can easily find m2 since m2 = 2m1.
After solving, we obtain two possible slopes for m1 (which may include both positive and negative values), and subsequently, we obtain the corresponding slopes for m2. The exact values can be found using algebraic techniques such as factorization or the quadratic formula if the equation turns into a quadratic.