It's not possible to answer clearly without knowing where the equality sign is meant to be in the question - next time write "equals" in the question please.
Because you did not supply the image, we cannot see the symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "equals". The question is about "yx" which is not a mapping and so does not have a slope.
y = x is a straight line through the origin, with a slope of 45 degrees (going from bottom left to top right).y = yx comprises two lines:y = 0 which is the x axis, andx = 1, which is a line parallel to the y axis, and at a distance 1 to its right.
It is (6, -1).
If you mean y = x+2 then the equation of y = x+4 is parallel to it because they both have the same slope but with different y intercepts
The slope of a line perpendicular to one with slope m is -1/m. So for a line with slope 1/7, any line perpendicular to it will have: slope = -1 / (1/7) = -7