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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. 361 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
role="math" localid="1648190660015" $4 x + 4 y = 8; x + y = 2$

Short Answer

Expert verified

The lines are parallel.

Step by step solution

01

Given information

The given equations are shown below:

$4 x + 4 y = 8 x + y = 2$

02

Solve both the equations for y

Solve $4 x + 4 y = 8$ for $y$ .

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

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

role="math" localid="1648191587301" $y = 2 - x y = - x + 2$

03

Determine the slope

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

localid="1648192887973" $m_{1} = - 1, c_{1} = 2$

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

localid="1648192895800" $m_{2} = - 1, c_{2} = 2$

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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