How to find the slope of line2 if the slope of line1 and angle of line2 is given?

Question

The measure of the angle from a line l1, with slope -1/3 to a line l2 is 135°. Find the slope of the line l2?

Answer 1

It may help to draw the picture of these two lines.  Choose L1 as passing through the Origin.

The slope of L1 enables us to calculate the angle that L1 makes with the x-axis: arctangent(-1/3) = -18.435⁰

 

Now you should be able to determine the desired angle θ that L2 makes with the x-axis, and from that, take tan θ

to get L2's slope. Much depends on the diagram that you draw...i.e. upon the direction of measuring the 135 degrees (of rotation from L1 to produce L2).