Q. 3.32 Identify the slope and y-interce... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 3: Q. 3.32 (page 263)

Identify the slope and $y -$ intercept from the equation of a line.
(a)
$y = - \frac{4}{3} x + 1$
(b)
$3 x + 2 y = 12$

Short Answer

Expert verified

(a)

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

$y -$ intercept is $(0, 1)$

(b)

Slope is $m = - \frac{3}{2}$

$y -$ intercept is $(0, 6)$

Step by step solution

Step 1. Given information

The equation of a line is

(a)

$y = - \frac{4}{3} x + 1$

(b)

$3 x + 2 y = 12$

Step 2. Finding slope and intercept of (a)

(a)

The equation of a line is

$y = - \frac{4}{3} x + 1$

Compare with slope-intercept formula

$y = m x + b$

So,

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

$b = 1$

So,

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

$y -$ intercept is $(0, 1)$

Step 3. Write the equation of a line in slope-intercept form for (b)

(b)

Write the equation in slope-intercept form.

So, solve for $y$

$3 x + 2 y = 12$

Subtract both sides $3 x$

$3 x + 2 y - 3 x = 12 - 3 x$

$2 y = - 3 x + 12$

Divide both sides $2$

$\frac{2 y}{2} = - \frac{3}{2} x + \frac{12}{2} y = - \frac{3}{2} x + 6$

Step 4. Finding slope and intercept of (b)

The slope-intercept form of a line is

$y = - \frac{3}{2} x + 6$

Compare with the slope-intercept formula of a line

$y = m x + b$

So,

$m = - \frac{3}{2} b = 6$

So,

slope is $- \frac{3}{2}$

$y -$ intercept is $(0, 6)$

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Identify the slope and $y -$ intercept from the equation of a line.
(a)
$y = - \frac{4}{3} x + 1$
(b)
$3 x + 2 y = 12$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding slope and intercept of (a)

Step 3. Write the equation of a line in slope-intercept form for (b)

Step 4. Finding slope and intercept of (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

91影视

Identify the slope and y-intercept from the equation of a line.(a)y=-43x+1(b)3x+2y=12

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding slope and intercept of (a)

Step 3. Write the equation of a line in slope-intercept form for (b)

Step 4. Finding slope and intercept of (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

Identify the slope and $y -$ intercept from the equation of a line.
(a)
$y = - \frac{4}{3} x + 1$
(b)
$3 x + 2 y = 12$