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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. 360 (page 522)

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

Short Answer

Expert verified

The lines are parallel.

Step by step solution

01

Given information

The given equations are shown below:

$x - y = 2 2 x - 2 y = 4$

02

Solve both equations for y

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

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

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

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

03

Determine the slope

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

localid="1648192806869" $m_{1} = 1, c_{1} = - 2$

Compare $y = x - 2$ with $y = m_{2} x + c_{2}$ .

localid="1648192817556" $m_{2} = 1, c_{2} = - 2$

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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