Use implicit differentiation to write the slope-intercept equation of the tangent line to the graph of (x^2+4)y=8 at the point (2,1):

(x^2+4) dy/dx + y(2 x dx/dx) = 0

(x^2+4) dy + 2 x y dx = 0
dy/dx = -2 x y/(x^2+4)
at (2,1)
dy/dx = -2(2)/(5) = -4/5 = slope = m

y = (-4/5) x + b
1 = (-4/5)+ b
b = 9/5
so
y = (-4/5) x + 9/5
5 y = -4 x + 9