Respuesta :
Given the equation:
[tex]y=5x+11[/tex]Let's find a set of parametric equation for the given equation given the parameter:
[tex]t=2-x[/tex]From the parameter:
t = 2 - x
Rewrite the parameter for x.
Rearrange the parameter:
[tex]2-x=t[/tex]Subtract 2 from both sides:
[tex]\begin{gathered} 2-2-x=t-2 \\ \\ -x=t-2 \end{gathered}[/tex]Divide all terms by -1:
[tex]\begin{gathered} \frac{-x}{-1}=\frac{t}{-1}-\frac{2}{-1} \\ \\ x=-t+2 \\ \\ x=2-t \end{gathered}[/tex]Now, substitute (2 - t) for x in the given equation:
[tex]\begin{gathered} y=5x+11 \\ \\ y=5(2-t)+11 \end{gathered}[/tex]Simplify the equation using distributive property:
[tex]\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}[/tex]Therefore, the set of parametric equations is:
• x = 2 - t
,• y = -5t + 21
ANSWER:
• x = 2 - t
,• y = -5t + 21
