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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. 368 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$7 x - 4 y = 8; 4 x + 7 y = 14$

Short Answer

Expert verified

The lines are not parallel.

Step by step solution

01

Given information

The given equations are shown below:

$7 x - 4 y = 8 4 x + 7 y = 14$

02

Solve both the equations for y

Solve $7 x - 4 y = 8$ for $y$ .

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

Solve $4 x + 7 y = 14$ for $y$ .

$\begin{array}{rcl} 7 y & = & 14 - 4 x \\ y & = & - \frac{4 x}{7} + \frac{14}{7} \\ y & = & - \frac{4}{7} x + 2 \end{array}$

03

Determine the slope

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

$m_{1} = \frac{7}{4}, c_{1} = - 2$

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

$m_{2} = - \frac{4}{7}, c_{2} = 2$

Here, $m_{1} 鈮� m_{2}$ .

The slopes are different and $y$ -intercept are different.

04

Write the conclusion

The lines are not parallel.

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Most popular questions from this chapter

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