Chapter 4.3, Problem 27E

To determine

To find: an equation that represents the new pipe.

Answer to Problem 27E

Therefore, the equation of the new pipe is $y=\frac{3}{2}-\frac{3}{4}x$

Explanation of Solution

Given:

Consider the following graph which represents the construction of the water pipe in the city below:

  

The objective is to find the equation that represents the new pipe.

Calculation:

Consider the equation of line L1 as $y-y_1=m\left(x-x_1\right)$

The slope of line which passes through points $\left(0,3\right)$ and $\left(-3,-1\right)$ is,

  $m=\frac{3-\left(-1\right)}{0-\left(-3\right)}$

  $=\frac{4}{3}$

The equation of line L1 is,

  $\begin{array}{l}y-3=\frac{4}{3}\left(x-0\right)\\ \text{ y=}\frac{4x}{3}+3\end{array}$

Find the equation of line L2.

Since the two lines are perpendicular, the slope of L2 is $-\frac{1}{m}$

The equation of line L2 which passes through the point $\left(2,0\right)$ is $y-y_1=-\frac{1}{m}\left(x-x_1\right)$

Use the above formula to find the equation line passing through $\left(2,0\right)$ and slope $m=\frac{4}{3}$

Therefore,

  $y-y_1=-\frac{1}{m}\left(x-x_1\right)$

  $\begin{array}{l}y-0=-\frac{3}{4}\left(x-2\right)\\ y=\frac{3}{2}-\frac{3}{4}x\end{array}$

Conclusion:

Therefore, the equation of the new pipe is $y=\frac{3}{2}-\frac{3}{4}x$