a. Answer Slope of L is -1. Explanation Given information: Consider the point P ( − 2 , 1 ) and the line L. x + y = 2 . Formula used: The equation of the line having slope m, and y −intercept b is: y = m x + b Calculation: Equation of the line L is: x + y = 2 y = − x + 2 ⇒ m = − 1 and b = 2 Therefore, slope of L is -1. b. To determine To write: an equation for the line through P and parallel to L. Answer An equation for the line through P and parallel to L is x + y = − 1 . Explanation Given information: Formula used: The equation of the line having slope m and passes through p ( x 1 , y 1 ) is: ( y − y 1 ) = m ( x − x 1 ) Calculation: Equation of the line L is: x + y = 2 y = − x + 2 ⇒ m = − 1 and b = 2 Parallel lines have the same slope so the line parallel to line L also have slope -1. Therefore, the equation of the line having slope -1 and passes through P ( − 2 , 1 ) is: ( y − 1 ) = − 1 ( x − ( − 2 ) ) y − 1 = − x − 2 y = − x − 1 x + y = − 1 Therefore, the equation for the line through P and parallel to L is x + y = − 1 . c. To determine To write: an equation for the line through P and perpendicular to L. Answer An equation for the line through P and Perpendicular to L is y − x = 3. Explanation Given information: Formula used: The equation of the line having slope m and passes through p ( x 1 , y 1 ) is: ( y − y 1 ) = m ( x − x 1 ) Calculation: Equation of the line L is: x + y = 2 y = − x + 2 ⇒ m = − 1 and b = 2 Perpendicular lines have the negative reciprocal slope so the line Perpendicular to line L has slope negative reciprocal of (-1) that is 1. Therefore, the equation of the line having slope 1 and passes through P ( − 2 , 1 ) is: ( y − 1 ) = 1 ( x − ( − 2 ) ) y − 1 = x + 2 y = x + 3 y − x = 3. Therefore, the equation for the line through P and Perpendicular to L is y − x = 3. d. To determine To find: the x-intercept of L. Answer The x-intercept of L is 2. Explanation Given information: The equation of line L is x + y = 2 . Calculation: The equation of line L is: x + y = 2 At x axis y = 0 ⇒ x + 0 = 2 ⇒ x = 2 Therefore, the x-intercept of L is 2.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Question

Chapter 1, Problem 68RE

To determine

To find: the slope of L.

Expert Solution

Answer to Problem 68RE

Slope of L is -1.

Explanation of Solution

Given information: Consider the point P(−2,1) and the line L. x+y=2 .

Formula used:

The equation of the line having slope m, and y −intercept b is:

y=mx+b

Calculation:

Equation of the line L is:

x+y=2y=−x+2⇒m=−1 and b=2

Therefore, slope of L is -1.

To determine

To write: an equation for the line through P and parallel to L.

Expert Solution

Answer to Problem 68RE

An equation for the line through P and parallel to L is x+y=−1 .

Explanation of Solution

Given information:

Formula used:

The equation of the line having slope m and passes through p(x1,y1) is:

(y−y1)=m(x−x1)

Calculation:

Equation of the line L is:

x+y=2y=−x+2⇒m=−1 and b=2

Parallel lines have the same slope so the line parallel to line L also have slope -1.

Therefore, the equation of the line having slope -1 and passes through P(−2,1) is:

(y−1)=−1(x−(−2))y−1=−x−2y=−x−1x+y=−1

Therefore, the equation for the line through P and parallel to L is x+y=−1 .

To determine

To write: an equation for the line through P and perpendicular to L.

Expert Solution

Answer to Problem 68RE

An equation for the line through P and Perpendicular to L is y−x=3.

Explanation of Solution

Given information:

Formula used:

The equation of the line having slope m and passes through p(x1,y1) is:

(y−y1)=m(x−x1)

Calculation:

Equation of the line L is:

x+y=2y=−x+2⇒m=−1 and b=2

Perpendicular lines have the negative reciprocal slope so the line Perpendicular to line L has slope negative reciprocal of (-1) that is 1.

Therefore, the equation of the line having slope 1 and passes through P(−2,1) is:

(y−1)=1(x−(−2))y−1=x+2y=x+3y−x=3.

Therefore, the equation for the line through P and Perpendicular to L is y−x=3.

To determine

To find: the x-intercept of L.

Expert Solution

Answer to Problem 68RE

The x-intercept of L is 2.

Explanation of Solution

Given information: The equation of line L is x+y=2.

Calculation:

The equation of line L is:

x+y=2At x axis y=0⇒x+0=2⇒x=2

Therefore, the x-intercept of L is 2.

Chapter 1, Problem 67RE

Chapter 1, Problem 69RE

Chapter 1 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

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