Question

Find a set of parametric equations for y= 5x + 11, given the parameter t=2-x

Answer 1

Given the equation:

`y=5x+11`

Let's find a set of parametric equation for the given equation given the parameter:

`t=2-x`

From the parameter:

t = 2 - x

Rewrite the parameter for x.

Rearrange the parameter:

`2-x=t`

Subtract 2 from both sides:

`\begin{gathered} 2-2-x=t-2 \\ \\ -x=t-2 \end{gathered}`

Divide all terms by -1:

`\begin{gathered} (-x)/(-1)=(t)/(-1)-(2)/(-1) \\ \\ x=-t+2 \\ \\ x=2-t \end{gathered}`

Now, substitute (2 - t) for x in the given equation:

`\begin{gathered} y=5x+11 \\ \\ y=5(2-t)+11 \end{gathered}`

Simplify the equation using distributive property:

`\begin{gathered} y=5(2)+5(-t)+11 \\ \\ y=10-5t+11 \\ \\ \text{ Collect like terms:} \\ y=-5t+10+11 \\ \\ y=-5t+21 \end{gathered}`

Therefore, the set of parametric equations is:

• x = 2 - t

,

• y = -5t + 21

ANSWER:

• x = 2 - t

,

• y = -5t + 21