(a) Answer The slope of the line 3 x + 4 y = 12 is − 3 4 . Explanation Given the equation of a line: 3 x + 4 y = 12 Concept Used: Slope-Intercept form of a line: Suppose that the equation of a line is given in the slope-intercept form: y = m x + c . Then, the m gives the slope of the line and c gives the y -intercept of the line. Calculation: Given the equation of the line: 3 x + 4 y = 12 . Write 3 x + 4 y = 12 in the slope-intercept form: 3 x + 4 y = 12 4 y = 12 − 3 x 4 y = − 3 x + 12 y = − 3 x + 12 4 y = − 3 4 x + 12 4 y = − 3 4 x + 3 . Thus, the slope-intercept form of the line: y = − 3 4 x + 3 . Compare y = − 3 4 x + 3 with the general slope-intercept form and observe that the slope of the line is − 3 4 . Conclusion: The slope of the line 3 x + 4 y = 12 is − 3 4 . (b) To determine To find the y -intercept of the line 3 x + 4 y = 12 . Answer The y -intercept of the line 3 x + 4 y = 12 is 3 . Explanation Given the equation of a line: 3 x + 4 y = 12 Concept Used: Slope-Intercept form of a line: Suppose that the equation of a line is given in the slope-intercept form: y = m x + c . Then, the m gives the slope of the line and c gives the y -intercept of the line. Calculation: Given the equation of the line: 3 x + 4 y = 12 . Write 3 x + 4 y = 12 in the slope intercept form: 3 x + 4 y = 12 4 y = 12 − 3 x 4 y = − 3 x + 12 y = − 3 x + 12 4 y = − 3 4 x + 12 4 y = − 3 4 x + 3 . Thus, the slope-intercept form of the line: y = − 3 4 x + 3 . Compare y = − 3 4 x + 3 with the general slope-intercept form and observe that the y -intercept of the line is 3 . Conclusion: The y -intercept of the line 3 x + 4 y = 12 is 3 . (c) To determine To graph the line 3 x + 4 y = 12 . Explanation Given the line: 3 x + 4 y = 12 Graph the line with the help of a graphing calculator:

Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020

6th Edition

ISBN: 9781418300203

Author: Prentice Hall

Publisher: Prentice Hall

See similar textbooks

Question

Chapter 0.1, Problem 25E

(a)

To determine

To find the slope of the line 3x+4y=12 .

(a)

Expert Solution

Answer to Problem 25E

The slope of the line 3x+4y=12 is −34 .

Explanation of Solution

Given the equation of a line:

3x+4y=12

Concept Used:

Slope-Intercept form of a line:

Suppose that the equation of a line is given in the slope-intercept form: y=mx+c .

Then, the m gives the slope of the line and c gives the y -intercept of the line.

Calculation:

Given the equation of the line:

3x+4y=12 .

Write 3x+4y=12 in the slope-intercept form:

3x+4y=124y=12−3x4y=−3x+12y=−3x+124y=−34x+124y=−34x+3 .

Thus, the slope-intercept form of the line:

y=−34x+3 .

Compare y=−34x+3 with the general slope-intercept form and observe that the slope of the line is −34 .

Conclusion:

The slope of the line 3x+4y=12 is −34 .

(b)

To determine

To find the y -intercept of the line 3x+4y=12 .

(b)

Expert Solution

Answer to Problem 25E

The y -intercept of the line 3x+4y=12 is 3 .

Explanation of Solution

Given the equation of a line:

3x+4y=12

Concept Used:

Slope-Intercept form of a line:

Suppose that the equation of a line is given in the slope-intercept form: y=mx+c .

Then, the m gives the slope of the line and c gives the y -intercept of the line.

Calculation:

Given the equation of the line:

3x+4y=12 .

Write 3x+4y=12 in the slope intercept form:

3x+4y=124y=12−3x4y=−3x+12y=−3x+124y=−34x+124y=−34x+3 .

Thus, the slope-intercept form of the line:

y=−34x+3 .

Compare y=−34x+3 with the general slope-intercept form and observe that the y -intercept of the line is 3 .

Conclusion:

The y -intercept of the line 3x+4y=12 is 3 .

(c)

To determine

To graph the line 3x+4y=12 .

(c)

Expert Solution

Explanation of Solution

Given the line:

3x+4y=12

Graph the line with the help of a graphing calculator:

Chapter 0.1, Problem 24E

Chapter 0.1, Problem 26E

Chapter 0 Solutions

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