Question

eliminate the parameter t to find a simplified cartesian equation of the form y = mx + b for \

$$\begin{cases} x(t) = -17 - t \\\\ y(t) = 2 - 2t \\end{cases}$$

the cartesian equation is y = \boxed{} question help: \boxed{video}

Explanation:

Step1: Solve for \( t \) from \( x(t) \)

Given \( x(t) = -17 - t \), we can rewrite it to solve for \( t \).
Adding \( t \) to both sides and subtracting \( x(t) \) from both sides, we get:
\( t = -17 - x(t) \)
We can just write \( t=-17 - x \) (since we will substitute into \( y(t) \) and we can use \( x \) instead of \( x(t) \) for the Cartesian equation).

Step2: Substitute \( t \) into \( y(t) \)

We know that \( y(t) = 2 - 2t \). Substitute \( t=-17 - x \) into this equation.
\( y = 2-2(-17 - x) \)
First, distribute the -2:
\( y=2 + 34+2x \)
Then, combine like terms:
\( y = 2x+36 \)

Answer:

\( 2x + 36 \)