Question

consider the following parametric equations:

$x = \frac{t}{-3}$ and $y = t^{2}-3$

step 1 of 2: eliminate the parameter $t$. please write your answer in simplest form solved for $y$.

Explanation:

Step1: Solve for \( t \) from \( x \) equation

Given \( x=\frac{t}{-3} \), multiply both sides by \(-3\) to get \( t=-3x \).

Step2: Substitute \( t \) into \( y \) equation

Substitute \( t = - 3x \) into \( y=t^{2}-3 \). Then \( y=(-3x)^{2}-3 \).
Simplify \( (-3x)^{2}-3 \):
Using the formula \((ab)^2=a^{2}b^{2}\), \((-3x)^{2}=(-3)^{2}x^{2}=9x^{2}\). So \( y = 9x^{2}-3 \).

Answer:

\( y=9x^{2}-3 \)