Answer
Cartesian equation: $x = y^{\frac 2 3}$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/59d31874-e3ca-4480-8f36-5158a339489d/result_image/1550774255.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20250215%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20250215T142237Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=3f293de84c6201cc8c3d20dba585d48a754f1f1a2a63068a69a91f3130361735)
Work Step by Step
(a)
1. Plot points determined by values for $t$. I used -3, -2, -1, 0, 1, 2 and 3.
2. Join them to produce a curve.
3. Draw the arrows indicating which direction the curve goes from $t = -3$ to $t= 3$
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(b)
Solve for $t$ in the second equation:
$y = t^3$
$\sqrt[3] y = t$
Substitute this value into the first equation:
$x = t^2$
$x = (\sqrt [3] y)^2 = y^{\frac{2}{3}}$