I solved this problem by checking if the two equations have the same coefficients/slopes. With different slopes, the lines form different angles with the axes. Since these lines are not parallel, they are not similar. Is this a sufficient mental calculation, or should I do the actual calculation?
What about y = x - 2 and y = -x -2?
Thanks; that’s a really interesting question. Since the slopes are opposites, I sketched them to see what happens. The triangles turn out to be mirror images of each other, so they’re still similar. The sign just flips the orientation, not the shape. So triangles formed with the axes are similar when the lines have the same absolute value of slope.