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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. 365 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$4 x - 8 y = 16; x - 2 y = 4$

Short Answer

Expert verified

The lines are parallel.

Step by step solution

01

Given information

The given equations are shown below:

$4 x - 8 y = 16 x - 2 y = 4$

02

Solve both the equations for y

Solve $4 x - 8 y = 16$ for $y$ .

$\begin{array}{rcl} - 8 y & = & 16 - 4 x \\ y & = & - \frac{4 x}{- 8} + \frac{16}{- 8} \\ y & = & \frac{1}{2} x - 2 \end{array}$

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

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

03

Determine the slope

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

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

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

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

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

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

04

Write the conclusion

The lines are 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, complete the table to find the solutions to each linear equation :

$y = 3 x - 1$

x	y	(x,y)
0
2
-1

Plot each point: 鈸� $(鈭� 5, 0)$ 鈸� $(3, 0)$ 鈸� $(0, 0)$ 鈸� $(0, 鈭� 1)$ 鈸� $(0, 4)$

Find the intercepts for $x + 2 y = 8$

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

See all solutions

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