Chapter 8.6, Problem 27E

To determine

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

Answer to Problem 27E

  $y=\frac{1}{4}x+\frac{23}{4}$

Explanation of Solution

Given information:

Parametric equations:

  $x=4t-11$  … (1)

  $y=t+3$  … (2)

Calculation:

Solve equation (1) for $t$ as shown below.

  $\begin{array}{c}x=4t-11\\ x+11=4t\left[\text{Add 11 on each side}\right]\\ t=\frac{1}{4}x+\frac{11}{4}\left[\text{Divide each side by 4}\right]\end{array}$

Now plug the value of $t$ in equation (2) to get the slope intercept equation as shown below.

  $\begin{array}{c}y=\left(\frac{1}{4}x+\frac{11}{4}\right)+3\\ =\frac{1}{4}x+\frac{11+12}{4}\\ =\frac{1}{4}x+\frac{23}{4}\end{array}$

Thus the slope intercept form of line with the given parametric equations is $y=\frac{1}{4}x+\frac{23}{4}$ .