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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. 349 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$6 x - 3 y = 9; 2 x - y = 3$

Short Answer

Expert verified

The lines are parallel.

Step by step solution

01

Given information

The given equations are shown below:

$6 x - 3 y = 9 2 x - y = 3$

02

Solve both equations for y.

Solve $6 x - 3 y = 9$ for $y$ .

$\begin{array}{rcl} - 3 y & = & 9 - 6 x \\ y & = & - \frac{6}{- 3} x + \frac{9}{- 3} \\ y & = & 2 x - 3 \end{array}$

Solve $2 x - y = 3$ for $y$ .

$\begin{array}{rcl} - y & = & 3 - 2 x \\ y & = & 2 x - 3 \end{array}$

03

Determine the slope.

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

localid="1648192563110" $m_{1} = 2, c_{1} = - 3$

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

localid="1648192574039" $m_{2} = 2, c_{2} = - 3$

Here, $m_{1} = m_{2}$ .

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

04

Write the conclusion

The lines are parallel.

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