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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. 348 (page 522)

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

Short Answer

Expert verified

The lines are parallel.

Step by step solution

01

Given information

The given equations are shown below:

$2 x - 4 y = 6 x - 2 y = 3$

02

Solve the equations for y

Solve $2 x - 4 y = 6$ for $y$ .

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

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

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

03

Determine the slope.

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

localid="1648192508377" $m_{1} = \frac{1}{2}, c_{1} = - \frac{3}{2}$

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

localid="1648192519547" $m_{2} = \frac{1}{2}, c_{2} = - \frac{3}{2}$

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

The slope are same and $y$ -intercept are same.

04

Write the conclusion

The lines are parallel.

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