Step 1

Given:

The rectangular equation is:

\(y=6x−5\)

We have to find the two different sets of parametric equations for a given rectangular equation.

Step 2

Now Consider,

t is a parameter for the given rectangular equation.

\(x=t\Rightarrow y=6t-5\)

Then the set is:

\({(x,y)|x=t\ and\ y = 6t-5}\)

Consider,

t is a parameter for the given rectangular equation.

\(x=t+2\)

\(\Rightarrow y=6(t+2)-5\)

\(\Rightarrow y=6t+12-5\)

\(\Rightarrow y=6t+7\)

Then the set is:

\({(x,y)|x=t+2\ and\ y = 6t+7}\)

Hence, the two different sets of parametric equations for a given rectangular equation are:

\({(t,6t-5)x=t\ and\ y=6t-5}\ and\ {((t+2),(6t+5))|x=t+2\ and\ y = 6t+7}\)