Chapter 1.5, Problem 17E

To determine

To find: whether graphs of given equations are parallel, coinciding, perpendicular, or none of these.

Answer to Problem 17E

Perpendicular

Explanation of Solution

Given information:

  $\begin{array}{l}4x-6y=11\mathrm{...}(1)\\ 3x+2y=9\mathrm{...}(2)\end{array}$

Calculation:

The slope-intercept equation is as follows:

  $y=mx+b$

Convert equation (1) in slope intercept form as shown below.

  $\begin{array}{l}4x-6y=11\\ -6y=-4x+11\\ y=\frac{-4}{-6}x+\frac{11}{6}\\ y=\frac{2}{3}x+\frac{11}{6}\end{array}$

Compare the above equation with slope intercept equation to get,

  $\begin{array}{l}m=\frac{2}{3}\\ b=\frac{11}{6}\end{array}$

Convert equation (2) in slope intercept form as shown below.

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

Compare above equation with slope intercept equation to get,

  $\begin{array}{l}m=-\frac{3}{2}\\ b=\frac{9}{2}\end{array}$

Since, the slope of both the lines is opposite reciprocal to each other i.e. $\left(\perp m=-\frac{1}{m}\right)$ . So, the two lines are perpendicular to each other.