Chapter 4: Q. 4.108 (page 515)

Use slopes and y-intercepts to determine if the lines $y = \frac{3}{4} x - 3$ and $3 x - 4 y = 12$ are parallel.

Short Answer

Expert verified

The equations are not parallel because they are the same line.

Step by step solution

Step 1. Given information.

The given equations are:

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

Step 2. Write the equation in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where m is the slope and $(0, b)$ is the y-intercept.

The first equation is already in slope-intercept form.

The second equation can be written as:

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

Step 3. Determine the slopes and y-intercepts.

For the first equation, $m = - \frac{3}{4}$ and the y-intercept is $(0, - 3)$ .

For the second equation, $m = - \frac{3}{4}$ and the y-intercept is $(0, - 3)$ .

The lines have the same slope, but they also have the same y-intercepts. Their equations represent the same line. They are not parallel; they are the same line.

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.

Use slopes and y-intercepts to determine if the lines $y = \frac{3}{4} x - 3$ and $3 x - 4 y = 12$ are parallel.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the equation in slope-intercept form.

Step 3. Determine the slopes and y-intercepts.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Use slopes and y-intercepts to determine if the lines y=34x-3and 3x-4y=12are parallel.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the equation in slope-intercept form.

Step 3. Determine the slopes and y-intercepts.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Use slopes and y-intercepts to determine if the lines $y = \frac{3}{4} x - 3$ and $3 x - 4 y = 12$ are parallel.