x = 2t + 5, y = 3 + 4/t. a) Find dy/dx at (9.5) and b) find y in terms of x.

This is a standard parametric equations question, it is important that the methodology behind answering this question is understood.

For part a) we simply use the chain rule (dy/dx = dy/dt X dt/dx) and the result dy/dx = 1/(dx/dy). 

dy/dt = -4/(t^2)

dx/dt = 2 => dt/dx = 1/2

=> dy/dx = [-4/(t^2)] X 1/2 = -2/(t^2)

now chose either x or y to find the value of t

9 = 2t + 5 => t = 2

5 = 3 + 4/t => t = 2

finally, substitute t = 2 into dy/dx which gives dy/dx = -1/2

For part b) you need to rearrange either x or y to make t the subject, I recommend x because you want to end up with y as the subject.

x = 2t +5 => t = (x - 5) / 2

now substitute into the equation for y.

y = 3 +4/[(x - 5)/2]

= 3 +8/(x - 5)

= 3(x -5) / (x - 5) + 8/(x - 5)

= (3x -15 +8) / (x - 5)

= (3x - 7) / (x - 5)