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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. 381 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are perpendicular.
$8 x - 2 y = 7; 3 x + 12 y = 9$

Short Answer

Expert verified

The lines are perpendicular.

Step by step solution

01

Given information

The given equation are shown below:

$8 x - 2 y = 7 3 x + 12 y = 9$

02

Solve both the equation for y

First, solve $8 x - 2 y = 7$ for $y$ .

$\begin{array}{rcl} - 2 y & = & 7 - 8 x \\ y & = & - \frac{8}{- 2} x + \frac{7}{- 2} \\ y & = & 4 x - \frac{7}{2} \end{array}$

Second, solve $3 x + 12 y = 9$ for $y$ .

$\begin{array}{rcl} 12 y & = & 9 - 3 x \\ y & = & - \frac{3}{12} x + \frac{9}{12} \\ y & = & - \frac{1}{4} x + \frac{3}{4} \end{array}$

03

Determine the lines are perpendicular or not

Compare $\begin{array}{rcl} y & = & 4 x - \frac{7}{2} \end{array}$ with $y = m_{1} x + c_{1}$ .

$m_{1} = 4$

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

$m_{2} = - \frac{1}{4}$

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

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

04

Write the conclusion

The lines are perpendicular.

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