Question

consider the following parametric equations:

( x = sqrt { t - 2 } ) and ( y = 3 t + 1 )

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

Explanation:

Step1: Solve \(x = \sqrt{t - 2}\) for \(t\)

Square both sides: \(x^{2}=t - 2\), then \(t=x^{2}+2\).

Step2: Substitute \(t\) into \(y = 3t+1\)

Substitute \(t=x^{2}+2\) into \(y = 3t + 1\): \(y=3(x^{2}+2)+1\).

Step3: Simplify the expression

Expand and simplify: \(y = 3x^{2}+6 + 1=3x^{2}+7\). Since \(x=\sqrt{t - 2}\geq0\), the domain of \(x\) is \(x\geq0\).

Answer:

\(y = 3x^{2}+7,x\geq0\)