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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. 351 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$8 x + 6 y = 6; 12 x + 9 y = 12$

Short Answer

Expert verified

The lines are parallel.

Step by step solution

01

Given information

The given equations are shown below:

$8 x + 6 y = 6 12 x + 9 y = 12$

02

Solve both the equation for y

Solve $8 x + 6 y = 6$ for $y$ .

$\begin{array}{rcl} 6 y & = & 6 - 8 x \\ y & = & - \frac{8}{6} x + \frac{6}{6} \\ y & = & - \frac{4}{3} x + 1 \end{array}$

Solve $12 x + 9 y = 12$ for $y$ .

$\begin{array}{rcl} 9 y & = & 12 - 12 x \\ y & = & - \frac{12}{9} x + \frac{12}{9} \\ y & = & - \frac{4}{3} x + \frac{4}{3} \end{array}$

03

Determine the slope.

Compare $\begin{array}{rcl} y & = & - \frac{4}{3} x + 1 \end{array}$ with $y = m_{1} x + c_{1}$ .

localid="1648192689396" $m_{1} = - \frac{4}{3}, c_{1} = 1$

Compare $\begin{array}{rcl} y & = & - \frac{4}{3} x + \frac{4}{3} \end{array}$ with $y = m_{2} x + c_{2}$ .

localid="1648192698624" $m_{2} = - \frac{4}{3}, c_{2} = \frac{4}{3}$

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

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

04

Write the conclusion

The lines are parallel.

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Most popular questions from this chapter

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

$x + y = 8$

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

$5 x 鈭� 2 y = 10$

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

鈸� $(鈭� 1, 1)$ 鈸� $(鈭� 2, 鈭� 1)$ 鈸� $(2, 1)$ 鈸� $(1, 鈭� 4)$ 鈸� $(3, \frac{7}{2})$

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system :

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) $(- 6, - 1)$

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