Chapter 4.3, Problem 27E

To determine

To write: An equation that represent the new pipe.

Answer to Problem 27E

Equation of proposed water pipe $3x+4y=6$ .

Explanation of Solution

Given information: We are given figure of a graph in which one line represents existing water pipe and other line which is perpendicular to this line represents proposed water pipe.

Calculation: As the line of existing water pipe is passes through the points $(0,3)\mathrm{and}(-3,-1)$ .

Therefore slope of line is $\frac{-1-3}{-3-0}=\frac{-4}{-3}=\frac{4}{3}$ .

Let Slope of line of proposed water pipe is $=m_2$ .

As the line of proposed water pipe is perpendicular to existing water pipe line.

  $\begin{array}{l}{m}_1.m_2=-1\\ \frac{4}{3}.m_2=-1\\ m_2=\frac{-3}{4}\end{array}$

Equation of proposed water pipe is:

  $\begin{array}{l}y-0=\frac{-3}{4}(x-2)\\ 4y=-3x+6\\ 3x+4y=6\end{array}$

Thus Equation of proposed water pipe is $3x+4y=6$ .