# Find two different sets of parametric equations for the rectangular equation y = 6x − 5

Equations

Find two different sets of parametric equations for the rectangular equation $$y = 6x − 5$$

2021-05-22

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