Tangent to a parametrized curve

[archaic]

Homework Statement

Given $x=t^2-6$ and $y=t^3+3t$, what is the equation of the tangent to the curve when $t=3$.

Relevant Equations

$m=y'(t)/x'(t)$

$x(3)=9-6=3$, $y(3)=27+9=36$.
$\frac{y'(3)}{x'(3)}=\frac{3\times9+3}{2\times3}=\frac{30}{6}=5$.
$y=5(x-3)+36=5x+21$.

 

[haruspex]

Homework Statement:: Given $x=t^2-6$ and $y=t^3+3t$, what is the equation of the tangent to the curve when $t=3$.
Relevant Equations:: $m=y'(t)/x'(t)$

$x(3)=9-6=3$, $y(3)=27+9=36$.
$\frac{y'(3)}{x'(3)}=\frac{3\times9+3}{2\times3}=\frac{30}{6}=5$.
$y=5(x-3)+36=5x+21$.
View attachment 260822

I can only suggest the format is not as required. It says to type an equation, but 5x+21 is not such.

 

[archaic]

I can only suggest the format is not as required. It says to type an equation, but 5x+21 is not such.