Q6. Which of the following is an equ... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 10: Q6. (page 664)

Which of the following is an equation of the line perpendicular to $4 x 鈭� 2 y = 6$ and passing through $(4, 鈭� 4)$ ?
$F$ $y = 鈭� \frac{3}{4} x + 3$
$G$ $y = 鈭� \frac{3}{4} x 鈭� 1$
$H$ $y = 鈭� \frac{1}{2} x 鈭� 4$
$J$ $y = 鈭� \frac{1}{2} x 鈭� 2$

Short Answer

Expert verified

The equation of the line perpendicular to $4 x 鈭� 2 y = 6$ and passing through $(4, 鈭� 4)$ is

$y = 鈭� \frac{1}{2} x 鈭� 2$ .

Option $J$ is correct.

Step by step solution

Step 1. State the concept of equation of line in ‘Slope intercept form’.

Suppose 鈥� $m$ 鈥� is the slope of the a and 鈥� $c$ 鈥� is the y-intercept of a line , then the equation of the line in slope intercept form is given as,

$y = m x + c 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� 鈥� (1)$ .

Step 2. State the concept of equation of line in ‘Slope-point form’.

Suppose a line has a slope 鈥� $m$ 鈥� and passes through the point, then the equation of the line in slope point is given as,

$(y 鈭� y_{1}) = m (x 鈭� x_{1}) 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� 鈥� (2)$

Step 3. State the concept of ‘perpendicularity of two lines’.

If two lines are pendicular to each other, then the product of their slopes is equal to 鈥� $- 1$ 鈥�.

That is, suppose $m_{1}$ is the slope of line one and $m_{2}$ is the slope of line two,

Then $m_{1} (m_{2}) = 鈭� 1 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆€夆€夆€夆€夆€夆€夆€夆€夆€夆€夆€夆€夆€夆€夆€� 鈥� (3)$

Step 3. Calculate the equation of the line perpendicular to 4x−2y=6 and passing through (4,−4).

First write the equation $4 x 鈭� 2 y = 6$ in slope intercept form and find its slope.

$\begin{array}{l} 4 x 鈭� 2 y = 6 \\ 4 x 鈭� 6 = 2 y \\ 2 y = 4 x 鈭� 6 \\ \frac{2 y}{2} = \frac{4 x 鈭� 6}{2} \\ y = \frac{4 x}{2} 鈭� \frac{6}{2} \\ y = 2 x 鈭� 3 \end{array}$

On comparing $y = 2 x 鈭� 3$ with $y = m x + c$

The slope of the line $y = 2 x 鈭� 3$ is $m = 2$ .

Let $m_{1}$ be the slope of the line perpendicular to the line $y = 2 x 鈭� 3$ .

$\begin{array}{l} m (m_{1}) = 鈭� 1 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� [鲍蝉颈苍驳鈥夆赌� 3] \\ 2 (m_{1}) = 鈭� 1 \\ m_{1} = 鈭� \frac{1}{2} \end{array}$

The line passes through the point $(4, 鈭� 4)$ and has a slope $m_{1} = 鈭� \frac{1}{2}$ .

Substitute $(4, 鈭� 4)$ as $(x_{1}, y_{1})$ and $鈭� \frac{1}{2}$ as m in (2) and find the required equation.

Therefore, by slope point form

$\begin{array}{l} (y 鈭� (鈭� 4)) = 鈭� \frac{1}{2} (x 鈭� 4) \\ y + 4 = (鈭� \frac{1}{2}) (x) 鈭� (鈭� \frac{1}{2}) (4) \\ y + 4 = 鈭� \frac{1}{2} x + \frac{4}{2} \\ y + 4 = 鈭� \frac{1}{2} x + 2 \\ y = 鈭� \frac{1}{2} x + 2 鈭� 4 \\ y = 鈭� \frac{1}{2} x 鈭� 2 \end{array}$

Therefore, the required equation $y = 鈭� \frac{1}{2} x 鈭� 2$ .

Option $J$ is correct.

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

Which of the following is an equation of the line perpendicular to $4 x 鈭� 2 y = 6$ and passing through $(4, 鈭� 4)$ ?
$F$ $y = 鈭� \frac{3}{4} x + 3$
$G$ $y = 鈭� \frac{3}{4} x 鈭� 1$
$H$ $y = 鈭� \frac{1}{2} x 鈭� 4$
$J$ $y = 鈭� \frac{1}{2} x 鈭� 2$

Short Answer

Step by step solution

Step 1. State the concept of equation of line in ‘Slope intercept form’.

Step 2. State the concept of equation of line in ‘Slope-point form’.

Step 3. State the concept of ‘perpendicularity of two lines’.

Step 3. Calculate the equation of the line perpendicular to 4x−2y=6 and passing through (4,−4).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Probability and Statistics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

91影视

Which of the following is an equation of the line perpendicular to4x鈭�2y=6 and passing through(4,鈭�4)?Fy=鈭�34x+3Gy=鈭�34x鈭�1Hy=鈭�12x鈭�4Jy=鈭�12x鈭�2

Short Answer

Step by step solution

Step 1. State the concept of equation of line in ‘Slope intercept form’.

Step 2. State the concept of equation of line in ‘Slope-point form’.

Step 3. State the concept of ‘perpendicularity of two lines’.

Step 3. Calculate the equation of the line perpendicular to 4x−2y=6 and passing through (4,−4).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Probability and Statistics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Which of the following is an equation of the line perpendicular to $4 x 鈭� 2 y = 6$ and passing through $(4, 鈭� 4)$ ?
$F$ $y = 鈭� \frac{3}{4} x + 3$
$G$ $y = 鈭� \frac{3}{4} x 鈭� 1$
$H$ $y = 鈭� \frac{1}{2} x 鈭� 4$
$J$ $y = 鈭� \frac{1}{2} x 鈭� 2$