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

Given information

The given equation are shown below:

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

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 $y$ .

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

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 $y = m_{2} x + c_{2}$ .

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

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

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

Write the conclusion

The lines are not perpendicular.

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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

Step by step solution

Given information

Solve both the equation for y

Determine the lines are perpendicular or not

Write the conclusion

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

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

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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