You should learn how to check it yourself. If [tex]x= 2[/math and in your formula for the plane give z= 3? Is the "x-slope", the coefficient of x in the plane formula, equal to ? Is the coefficient of y in theplane formula equal to ?
Here, by the way is what I consider to be a simpler way to find the tangent plane to . The function has or as a "level surface". The gradient of g, is perpendicular to that level surface and so perpendicular to its tangent plane, the tangent plane to z= f(x,y).
If a normal to a plane at is [tex]\nabla g= <-f_x, -f_y, 1>[tex], then the plane is given by