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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. 369 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$9 x - 5 y = 4; 5 x + 9 y = - 1$

Short Answer

Expert verified

The lines are not parallel.

Step by step solution

01

Given information

The given equations are shown below:

$9 x - 5 y = 4 5 x + 9 y = - 1$

02

Solve both the equations for y.

Solve $9 x - 5 y = 4$ for $y$ .

$\begin{array}{rcl} - 5 y & = & 4 - 9 x \\ y & = & - \frac{9 x}{- 5} + \frac{4}{- 5} \\ y & = & \frac{9}{5} x - \frac{4}{5} \end{array}$

Solve $5 x + 9 y = - 1$ for $y$ .

$\begin{array}{rcl} 9 y & = & - 1 - 5 x \\ y & = & - \frac{5 x}{9} - \frac{1}{9} \end{array}$

03

Determine the slope.

Compare $\begin{array}{rcl} y & = & \frac{9}{5} x - \frac{4}{5} \end{array}$ with $y = m_{1} x + c_{1}$ .

$m_{1} = \frac{9}{5}, c_{1} = - \frac{4}{5}$

Compare $\begin{array}{rcl} y & = & - \frac{5 x}{9} - \frac{1}{9} \end{array}$ with $y = m_{2} x + c_{2}$ .

$m_{2} = - \frac{5}{9}, c_{2} = - \frac{1}{9}$

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

In the following exercises, which ordered pairs are solutions to the given equations :

$y = \frac{1}{3} x + 1$

(a) $(- 3, 0)$ (b) $(9, 4)$ (c) $(- 6, - 1)$

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system :

Find an equation of a line with slope $m = \frac{2}{3}$ and containing the point $(9, 2)$ .

Find an equation of a line with slope $m = \frac{5}{6}$ and containing the point $(6, 3)$ .

In the following exercises, find three solutions to each linear equation.

$y = 鈭� 2 x + 7$

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