Chapter 11: Q. 2 (page 713)

(a) Graph the line : $3 x + 4 y = 12$ .
(b) What is the slope of a line parallel to this line?

Short Answer

Expert verified

(a) Graph of the line $3 x + 4 y = 12$ is shown below.

(b) The slope of the parallel line is $- \frac{3}{4}$ or $- 0.75$ .

Step by step solution

Part (a) Step 1. Given information.

The given equation is:

$3 x + 4 y = 12$

Part (a) Step 2. Determine the intercepts.

Substitute $x = 0$ to find y-intercept.

$\begin{array}{rcl} 3 (0) + 4 y & = & 12 \\ 4 y & = & 12 \\ y & = & \frac{12}{4} \\ y & = & 3 \end{array}$

Substitue $y = 0$ to find the x-intercept.

$\begin{array}{rcl} 3 x + 4 (0) & = & 12 \\ 3 x & = & 12 \\ x & = & \frac{12}{3} \\ x & = & 4 \end{array}$

So, graph intersect the x-axis at $(4, 0)$ and the y-axis at $(0, 3) .$

Part (a) Step 3. Draw the graph.

Plot the points $(0, 3)$ and $(4, 0)$ on a coordinate plane and connect them by a straight line.

Part (b) Step 1 Given information.

The given equation is:

$3 x + 4 y = 12$

Part (b) Step 2. Determine the slope of the parallel line.

The slope of the line $a x + b y = c$ is $m = - \frac{a}{b}$ .

In the given equation $a = 3, b = 4$ . So, the slope of the given line is:

$m = - \frac{3}{4}$

The slopes of parallel lines are always equal. It means the slope of the parallel is $- \frac{3}{4}$ or $- 0.75$ .

Part (b) Step 3. Conclusion.

The slope of the parallel line is $- \frac{3}{4}$ or $- 0.75$ .

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.

(a) Graph the line : $3 x + 4 y = 12$ .
(b) What is the slope of a line parallel to this line?

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Determine the intercepts.

Part (a) Step 3. Draw the graph.

Part (b) Step 1 Given information.

Part (b) Step 2. Determine the slope of the parallel line.

Part (b) Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

(a) Graph the line : 3x+4y=12.(b) What is the slope of a line parallel to this line?

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Determine the intercepts.

Part (a) Step 3. Draw the graph.

Part (b) Step 1 Given information.

Part (b) Step 2. Determine the slope of the parallel line.

Part (b) Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

(a) Graph the line : $3 x + 4 y = 12$ .
(b) What is the slope of a line parallel to this line?