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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. 378 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are perpendicular.
$4 x - 2 y = 5; 3 x + 6 y = 8$

Short Answer

Expert verified

The lines are perpendicular.

Step by step solution

01

Given information

The given equation are shown below:

$4 x - 2 y = 5 3 x + 6 y = 8$

02

Solve both the equation for y

First, solve $4 x - 2 y = 5$ for $y$ .

$\begin{array}{rcl} - 2 y & = & 5 - 4 x \\ y & = & - \frac{4}{- 2} x + \frac{5}{- 2} \\ y & = & 2 x - \frac{5}{2} \end{array}$

Second, solve $3 x + 6 y = 8$ for $y$ .

$\begin{array}{rcl} 6 y & = & 8 - 3 x \\ y & = & - \frac{3}{6} x + \frac{8}{6} \\ y & = & - \frac{1}{2} x + \frac{4}{3} \end{array}$

03

Determine the lines are perpendicular or not

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

$m_{1} = 2$

Compare $\begin{array}{rcl} y & = & - \frac{1}{2} x + \frac{4}{3} \end{array}$ with $y = m_{2} x + c_{2}$ .

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

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

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

04

Write the conclusion

The lines are perpendicular.

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