Chapter 8.7, Problem 25E

To determine

To find: the equation of line with given parametric equations in slope intercept form.

Answer to Problem 25E

  $y=6x-58$

Explanation of Solution

Given information:

  $\begin{array}{l}x=11-t\\ y=8-6t\end{array}$

Calculation:

Solve the equation of $x$ in terms of $t$ as shown below.

  $\begin{array}{c}x=11-t\\ x+t=11\left[\text{Add both sides by }t\right]\\ t=11-x\left[\text{Subtract }x\text{ from each side}\right]\end{array}$

Substitute $t$ in the parametric equation of $y$ as shown below.

  $\begin{array}{c}y=8-6t\\ =8-6\left(11-x\right)\\ =8-66+6x\\ =6x-58\end{array}$

Thus the slope intercept equation parametric with the given equation is $y=6x-58$ .