Well, since you are looking for the vertex, I am assuming you may have wrote the problem wrong because this equation is linear (meaning the highest degree is 1). Equations that have vertices are usually quadratic (highest degree is 2), for example y = x^2 + 5x - 2.
For the equation you provided, x = 12y + 21 + 2 can be simplified by added the 21 and 2, and then solving for y.
x = 12y + 23.
x - 23 = 12y
y = (x - 23)/12 = x/12 - 23/12
You can graph this by refering to slope-intercept form. y = mx + b, when m is the slope, and b is the y-intercept.
So slope is m = (1/12) and y-intercept is (0, 23/12).
The equation is linear, so their is no vertex or line of symmetry.