Chapter 4: Q. 373 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are perpendicular.
$2 x + 3 y = 5; 3 x - 2 y = 7$

Short Answer

Expert verified

The lines are perpendicular.

Step by step solution

Given information

The given equation are shown below:

$2 x + 3 y = 5 3 x - 2 y = 7$

Solve both the equation for y

First, solve $2 x + 3 y = 5$ for $y$ .

$\begin{array}{rcl} 3 y & = & 5 - 2 x \\ y & = & - \frac{2}{3} x + \frac{5}{3} \end{array}$

Second, solve $3 x - 2 y = 7$ for $y$ .

$\begin{array}{rcl} - 2 y & = & 7 - 3 x \\ y & = & - \frac{3}{- 2} x + \frac{7}{- 2} \\ y & = & \frac{3}{2} x - \frac{7}{2} \end{array}$

Determine the lines are perpendicular or not

Compare $\begin{array}{rcl} y & = & - \frac{2}{3} x + \frac{5}{3} \end{array}$ with $y = m_{1} x + c_{1}$ .

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

Compare $\begin{array}{rcl} y & = & \frac{3}{2} x - \frac{7}{2} \end{array}$ 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.

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In the following exercises, use slopes and $y$ -intercepts to determine if the lines are perpendicular.
$2 x + 3 y = 5; 3 x - 2 y = 7$

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.2x+3y=5;3x-2y=7

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

Geometry

Statistics

Logic and Functions

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are perpendicular.
$2 x + 3 y = 5; 3 x - 2 y = 7$