A particle moves in the plane so that, for each real number t, its position is given by the parametric equations
x(t)=t2+1,y(t)=3t−2.
Answer the following questions about the motion of the particle.
a. Determine the coordinates of the particle when t=2.
b. Find dxdy at t=2.
c. Using your results, write the equation of the tangent line to the particle’s path at t=2 in point–slope form.
d. Rewrite the equation from part (c) in slope–intercept form.