The parametric equations of a curve are $$\[ x=\ln (2+3 t), \quad y=\frac{t}{2+3 t} . \]$$ Find the equation of the tangent to the curve at the point where it intersects the $$$y$$$-axis. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_31 Year：2021 Question No：6(b)

Answer:

Obtain $y=-\frac{1}{3}$ when $x=0$
Use a correct method to form the given tangent
Obtain answer $3 y=2 x-1$

3.4.3 find and use the first derivative of a function which is defined parametrically or implicitly.