Question

If a line has slope​ a, what is the slope of its reflection across the line y​=x?

Answer 1

Check the picture below.

notice the reflected gray line on the red one over the y=x line, the slope of either line across the y=x line is simply the other's upside-down.

$\stackrel{\textit{slope of line "a"}}{a\implies \cfrac{a}{1}}\hspace{5em}\stackrel{\textit{slope of its reflection}}{\cfrac{1}{a}}$