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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. 345 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$y = \frac{2}{3} x - 1; 2 x - 3 y = - 2$

Short Answer

Expert verified

The lines are parallel.

Step by step solution

01

Given information

The given equations are shown below:

$y = \frac{2}{3} x - 1 2 x - 3 y = - 2$

02

Solve both the equations for y.

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

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

03

Determine the slope of the equations.

Compare $y = \frac{2}{3} x - 1$ with $y = m_{1} x + c_{1}$ .

localid="1648192246923" $m_{1} = \frac{2}{3}, c_{1} = - 1$

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

localid="1648192258414" $m_{2} = \frac{2}{3}, c_{2} = \frac{2}{3}$

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

Since, the slopes are same but $y$ -intercept is different.

04

Write the conclusion

The lines are parallel.

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