Chapter 12.3, Problem 45STP

To determine

To find:

The slope of a line perpendicular to the given line.

Answer to Problem 45STP

The option D is correct.

Explanation of Solution

Given information:

Equation of line is $2x+3y=9$ .

Calculation:

Equation of line is $2x+3y=9$ .

First write the equation in the slope intercept form.

  $\begin{array}{l}2x+3y=9\\ 3y=-2x+9\\ y=\left(\frac{-2}{3}\right)x+\frac{9}{3}\\ y=\left(\frac{-2}{3}\right)x+3\end{array}$

The slope of the given line is $\frac{-2}{3}$ .

The product of slopes of perpendicular lines is $-1$ .

Assume that the other slope be $m$ .

  $\begin{array}{c}m\left(\frac{-2}{3}\right)=-1\\ m\left(\frac{2}{3}\right)=1\\ m\left(\frac{2}{3}\right)\frac{3}{2}=1\cdot \frac{3}{2}\\ m=\frac{3}{2}\end{array}$

Hence, the option D is correct.