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

Given information

The given equations are shown below:

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

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 $y$ .

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

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.

Write the conclusion

The lines are parallel.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Step by step solution

Given information

Solve both equations for y

Determine the slope

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Calculus

Statistics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

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

Short Answer

Step by step solution

Given information

Solve both equations for y

Determine the slope

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Calculus

Statistics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

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