Chapter 4: Q. 370 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are perpendicular.
$3 x - 2 y = 8; 2 x + 3 y = 6$

Short Answer

Expert verified

The lines are perpendicular.

Step by step solution

Given information

The given equation are shown below:

$3 x - 2 y = 8 2 x + 3 y = 6$

Solve both the equation for y

First, solve $2 x + 3 y = 6$ for $y$ .

role="math" localid="1647963938545" $\begin{array}{rcl} 3 y & = & 6 - 2 x \\ y & = & - \frac{2}{3} x + \frac{6}{3} \\ y & = & - \frac{2}{3} x + 2 \end{array}$

Second, solve $3 x - 2 y = 8$ for $y$ .

role="math" localid="1647963944067" $\begin{array}{rcl} - 2 y & = & 8 - 3 x \\ y & = & - \frac{3}{- 2} x + \frac{8}{- 2} \\ y & = & \frac{3}{2} x - 4 \end{array}$

Determine the lines are perpendicular or not

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

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

Compare $\begin{array}{rcl} y & = & \frac{3}{2} x - 4 \end{array}$ with $y = m_{2} x + c_{2}$ .

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

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

Since, the product of their slopes is $- 1$ .

Write the conclusion

The lines are perpendicular.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are perpendicular.
$3 x - 2 y = 8; 2 x + 3 y = 6$

Short Answer

Step by step solution

Given information

Solve both the equation for y

Determine the lines are perpendicular or not

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Pure Maths

Statistics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.3x-2y=8;2x+3y=6

Short Answer

Step by step solution

Given information

Solve both the equation for y

Determine the lines are perpendicular or not

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Pure Maths

Statistics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are perpendicular.
$3 x - 2 y = 8; 2 x + 3 y = 6$