SOLUTION: Find two different sets of parametric equations for the rectangular equation given. y=4x-5 ​(a) Let and determine the parametric equation for y for the given rectangular eq

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Question 1194462: Find two different sets of parametric equations for the rectangular equation given.
y=4x-5
​(a) Let and determine the parametric equation for y for the given rectangular equation.
y=____
  
​(b) Let and determine the parametric equation for y for the given rectangular equation.
y=____
  
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Start with this system
system%28x=t%2Cy=4t-5%29
It should be fairly clear that we can replace t with x to go from y = 4t-5 to y = 4x-5
Both x and t are placeholders for a variable. The naming of said variable isn't really important.

That is what I would consider a trivial solution.

A more interesting solution would have us replace each t with (t-1) to have...
  • x = t turn into x = t-1
  • y = 4t-5 turn into y = 4(t-1)-5 = 4t-4-5 = 4t-9
One possible answer for part (a) is
system%28x=t-1%2Cy=4t-9%29
Note that solving the first equation for t gets us
t = x+1
Then plug this into the second equation
y = 4t-9
y = 4(x+1)-9
y = 4x+4-9
y = 4x-5
which helps us confirm we have the correct set of equations.

Use this trick to find a possible set of parametric equations for part (b)
Go back to the original system mentioned at the top of this solution page. Then replace t with something like (t-2) and see what happens.
Feel free to use something more interesting or creative if you prefer.

If you wanted, you could use the first system as the answer since it technically fits the requirements (even if it's not all that interesting).