Chapter 4: Q. 4.112 (page 518)

Use slopes to determine if the lines $2 x - 9 y = 3$ and $9 x - 2 y = 1$ are perpendicular.

Short Answer

Expert verified

The slopes are not negative reciprocals of each other, so the lines are not perpendicular.

Step by step solution

Step 1. Given information.

The given equations are:

$\begin{array}{rcl} 2 x - 9 y & = & 3 \\ 9 x - 2 y & = & 1 \end{array}$

Step 2. Write first equations in slope-intercept form.

The first equation can be written as:

$\begin{array}{rcl} 2 x - 9 y & = & 3 \\ - 9 y & = & - 2 x + 3 \\ y & = & \frac{- 2 x + 3}{- 9} \\ y & = & \frac{2}{9} x - \frac{1}{3} \end{array}$

Step 3. Write second equations in slope-intercept form.

The second equation can be written as:

$\begin{array}{rcl} 9 x - 2 y & = & 1 \\ - 2 y & = & - 9 x + 1 \\ y & = & \frac{- 9 x + 1}{- 2} \\ y & = & \frac{9}{2} x - \frac{1}{2} \end{array}$

Step 4. Determine whether the lines are perpendicular or not.

Compare the slope intercepts forms of the equations with $y = m x + b$ .

For the first equation, $m_{1} = \frac{2}{9}$ .

For the second equation, $m_{2} = \frac{9}{2}$ .

If the product of slopes is $- 1$ , then the lines are perpendicular.

$\begin{array}{rcl} m_{1} \cdot m_{2} & = & \frac{2}{9} \cdot \frac{9}{2} \\ = & 1 \neq - 1 \end{array}$

The slopes are not negative reciprocals of each other, so the lines are not perpendicular.

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Use slopes to determine if the lines $2 x - 9 y = 3$ and $9 x - 2 y = 1$ are perpendicular.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write first equations in slope-intercept form.

Step 3. Write second equations in slope-intercept form.

Step 4. Determine whether the lines are perpendicular or not.

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Use slopes to determine if the lines 2x−9y=3 and9x−2y=1 are perpendicular.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write first equations in slope-intercept form.

Step 3. Write second equations in slope-intercept form.

Step 4. Determine whether the lines are perpendicular or not.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Mechanics Maths

Statistics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use slopes to determine if the lines $2 x - 9 y = 3$ and $9 x - 2 y = 1$ are perpendicular.