Question

A tangent line to the curve c(t)=(2t^2−3t+5,t^3+9t−1) has slope −3 at the point(s)

Answer 1

slope is change in y divided by change in x

you have c(t) = (x(t), y(t) )
I would find dy/dt / dx/dt
and set that equal to -3 and solve for t