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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. 371 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are perpendicular.
$x - 4 y = 8; 4 x + y = 2$

Short Answer

Expert verified

The lines are perpendicular.

Step by step solution

01

Given information

The given equation are shown below:

$x - 4 y = 8 4 x + y = 2$

02

Solve both the equation for y

First, solve $x - 4 y = 8$ for $y$ .

role="math" localid="1647964053380" $\begin{array}{rcl} - 4 y & = & 8 - x \\ y & = & - \frac{x}{- 4} + \frac{8}{- 4} \\ y & = & \frac{x}{4} - 2 \end{array}$

Second solve $4 x + y = 2$ for $y$ .

role="math" localid="1647964077415" $\begin{array}{rcl} y & = & 2 - 4 x \\ y & = & - 4 x + 2 \end{array}$

03

Determine the lines are perpendicular or not

Compare $\begin{array}{rcl} y & = & \frac{x}{4} - 2 \end{array}$ with $y = m_{1} x + c_{1}$ .

$m_{1} = \frac{1}{4}$

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

$m_{2} = - 4$

$\begin{array}{rcl} m_{1} m_{2} & = & \frac{1}{4} 路 - 4 \\ = & - 1 \end{array}$

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

04

Write the conclusion

The lines are perpendicular.

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