Find a parametrization of the surface $x^3 + 7xy + z^2 = 9$ where $x > 0$ and use it to find the tangent plane at
$x = 2, y = \frac{1}{7}, z = 0$.
(Use symbolic notation and fractions where needed.)
$y = \frac{(28-13x)}{14}$
Incorrect Answer
Sorry, that's incorrect.
You have not correctly found the equation of the tangent plane.
You have two options here: you can solve the equation for $y = f(x, z)$ and then parametrize this as a graph as $(u, v) = (u, f (u, v), v)$ and proceed as normal. The other option is to treat this as a level surface and calculate the tangent plane that way. Do both and compare your results.