Answer
The equation of the tangent line to the graph at the given point (9,4)
is: y = -$\frac{2}{3}$x+10.
Work Step by Step
$\sqrt x$+ $\sqrt y$=5
$\sqrt x$= 5-$\sqrt x$
y=$(5-\sqrt x)^{2}$
y=25+x-10$\sqrt x$=f(x)
f'(x)=1-10$\frac{1}{2}$$x^{-\frac{1}{2}}$+0
f'(9)=-$\frac{2}{3}$
In order to find the equation we have to solve this linear system of equations:
{y=f'(9)+q , 4=-$\frac{2}{3}$(9)+q
and we obtain q=10.
So, y = -$\frac{2}{3}$x+10 is the requested equation.
