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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 4: Q. 374 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are perpendicular.
$3 x - 2 y = 1; 2 x - 3 y = 2$

Short Answer

Expert verified

The lines are not perpendicular.

Step by step solution

01

Given information

The given equation are shown below:

$3 x - 2 y = 1 2 x - 3 y = 2$

02

Solve both the equation for y

First, solve $3 x - 2 y = 1$ for $y$ .

$\begin{array}{rcl} - 2 y & = & 1 - 3 x \\ y & = & - \frac{3}{- 2} x + \frac{1}{- 2} \\ y & = & \frac{3}{2} x - \frac{1}{2} \end{array}$

Second, solve $2 x - 3 y = 2$ for $y$ .

$\begin{array}{rcl} - 3 y & = & 2 - 2 x \\ y & = & - \frac{2}{- 3} x + \frac{2}{- 3} \\ y & = & \frac{2}{3} x - \frac{2}{3} \end{array}$

03

Determine the lines are perpendicular or not

Compare $\begin{array}{rcl} y & = & \frac{3}{2} x - \frac{1}{2} \end{array}$ with $y = m_{1} x + c_{1}$ .

$m_{1} = \frac{3}{2}$

Compare $\begin{array}{rcl} y & = & \frac{2}{3} x - \frac{2}{3} \end{array}$ with $y = m_{2} x + c_{2}$ .

$m_{2} = \frac{2}{3}$

$\begin{array}{rcl} m_{1} m_{2} & = & \frac{3}{2} 路 \frac{2}{3} \\ = & 1 \end{array}$

Since, the product of their slopes is not equal $- 1$ .

04

Write the conclusion

The lines are not perpendicular.

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