French: What is the slope of the line?

What is the slope of the line?, №12148243, 22.03.2021 00:06

Mathematics

1. write the equation in slope-intercept form. identify the slope and y-intercept. show all work 2x - 3y = 9 2. write the equation in slope-intercept form. identify the slope and y-intercept. show all work x - 4y = -20 3. find the x- and y-intercepts for -x + 4y = 12. write each intercept as a unique ordered pair. show all work 4. y = 2/3x + 7 written in standard form using integers is 3x - y = 21. a) true b) false 5. write an equation of a line that has the same slope as 2x – 5y = 12 and the same y-intercept as 4y + 24 = 5x. a) y= 2/5x−6 b) y=6x−2/5

Step-by-step answer

P Answered by PhD

46

Part 1)

we know that

the equation of the line in slope-intercept form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

we have

2x-3y=9

solve for y

3y=2x-9

y=(2/3)x-3 -------> equation of the line in slope-intercept form

so

the slope m is $\frac{2}{3}$

the y-intercept b is

Part 2)

we know that

the equation of the line in slope-intercept form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

we have

x-4y=-20

solve for y

4y=x+20

y=(1/4)x+5 -------> equation of the line in slope-intercept form

so

the slope m is $\frac{1}{4}$

the y-intercept b is

Part 3)

we know that

The x-intercept is the value of x when the value of y is equal to zero

The y-intercept is the value of y when the value of x is equal to zero

we have

-x+4y=12

a) Find the x-intercept

For y=0 substitute in the equation

-x+4*0=12

x=-12

The answer part 3a) is (-12,0)

b) Find the y-intercept

For x=0 substitute in the equation

-0+4y=12

y=3

The answer part 3b) is (0,3)

Part 4)

we know that

the equation of the line in standard form is

Ax+By=C

we have

$y=\frac{2}{3}x+7$

Multiply by both sides

3y=2x+21

2x-3y=-21 ------> equation in standard form

therefore

the answer Part 4) is option B False

Part 5)

Step 1

Find the slope

we have

2x-5y=12

solve for y

5y=2x-12

y=(2/5)x-(12/5)

so

the slope m is $\frac{2}{5}$

Step 2

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

we have

4y+24=5x

for x=0

4y+24=5*0

4y=-24

y=-6

the y-intercept is

Step 3

Find the equation of the line

we have

$m=\frac{2}{5}$

b=-6

the equation of the line in slope-intercept form is

y=mx+b

substitute the values

$y=\frac{2}{5}x-6$

therefore

the answer Part 5) is the option A $y=\frac{2}{5}x-6$

Part 6)

Step 1

Find the slope of the given line

we know that

if two lines are perpendicular. then the product of their slopes is equal to minus one

so

m1*m2=-1

in this problem

the given line

x+8y=27

solve for y

8y=27-x

y=(27/8)-(x/8)

the slope m1 is $m1=-\frac{1}{8}$

so

the slope m2 is m2=8

Step 2

Find the equation of the line

we know that

the equation of the line in slope point form is equal to

y-y1=m*(x-x1)

we have

m2=8

point (-5,5)

substitutes the values

y-5=8*(x+5)

y=8x+40+5

y=8x+45

therefore

the answer part 6) is the option C y=8x+45

Part 7)

y=(8/3)x+ 19 -------> the slope is m=(8/3)

8x- y=17

y =8x-17 --------> the slope is m=8

we know that

if two lines are parallel , then their slopes are the same

in this problem the slopes are not the same

therefore

the answer part 7) is the option D) No, since the slopes are different.

Part 8)

a. Write an equation for the line in point-slope form

b. Rewrite the equation in standard form using integers

Step 1

Find the slope of the line

we know that

the slope between two points is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

substitute the values

$m=\frac{(4+1)}{(8-2)}$

$m=\frac{(5)}{(6)}$

Step 2

Find the equation in point slope form

we know that

the equation of the line in slope point form is equal to

y-y1=m*(x-x1)

we have

m=(5/6)

point (2,-1)

substitutes the values

y+1=(5/6)*(x-2) -------> equation of the line in point slope form

Step 3

Rewrite the equation in standard form using integers

y=(5/6)x-(5/3)-1

y=(5/6)x-(8/3)

Multiply by both sides

6y=5x-16

5x-6y=16 --------> equation of the line in standard form

Part 9)

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

where

(x1,y1) ------> is the first point

(x2,y2) -----> is the second point

In the numerator calculate the difference of the y-coordinates

in the denominator calculate the difference of the x-coordinates

Part 10)

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

substitutes

$m=\frac{(5+1)}{(-1+3)}$

$m=\frac{(6)}{(2)}$

m=3

therefore

the answer Part 10) is m=3

Part 11)

we know that

the equation of the line in slope point form is equal to

y-y1=m*(x-x1)

substitute the values

y+9=-2*(x-10) --------> this is the equation in the point slope form

Mathematics

Write an equation in point-slope form for the line through the given point with the given slope. (10, –9); m = –2 y + 9 = –2(x – 10) y – 10 = –2(x + 9) y – 9 = –2(x + 10) y – 9 = –2(x – 10) 2. are the graphs of the lines in the pair parallel? explain. y = 6x + 9 27x – 3y = –81 no, since the slopes are different. yes, since the slopes are the same and the y-intercepts are different. no, since the y-intercepts are different. yes, since the slopes are the same and the y-intercepts are the same. write the equation of a line that is perpendicular to

Step-by-step answer

P Answered by PhD

3

y -y1= m(x-x1) is in point slope form

y --9 = -2 (x-10)

y+9 = -2(x-10)

Mathematics

Write an equation in point-slope form for the line through the given point with the given slope. (10, –9); m = –2 y + 9 = –2(x – 10) y – 10 = –2(x + 9) y – 9 = –2(x + 10) y – 9 = –2(x – 10) 2. are the graphs of the lines in the pair parallel? explain. y = 6x + 9 27x – 3y = –81 no, since the slopes are different. yes, since the slopes are the same and the y-intercepts are different. no, since the y-intercepts are different. yes, since the slopes are the same and the y-intercepts are the same. write the equation of a line that is perpendicular to

Step-by-step answer

P Answered by PhD

3

y -y1= m(x-x1) is in point slope form

y --9 = -2 (x-10)

y+9 = -2(x-10)

Mathematics

Line ab contains points a (1, 2) and b (−2, 6) the slope of line ab is a)zero b)undefined c)positive d)negative the equation of line cd is (y−3) = − 2 (x − 4). what is the slope of a line perpendicular to line cd? line cd contains points a (4, 6) and b (−2, 6). the slope of line cd is line qr contains (2, 8) and (3, 10) line st contains points (0, 6) and (−2, 2). lines qr and st are the equation of line qr is y = negative 1 over 2x + 1. write an equation of a line perpendicular to line qr in slope-intercept form that contains point (5, 6). the

Step-by-step answer

P Answered by Specialist

18

On the first question, the formula would be m=\frac{y2-y1}{x2-x1} and the value we got is -4/3, so D.
On the second quesiton, the slope in the given equation of the line is -2, its negative reciprocal is 1/2, so A.
On the third question, use the slope formula above and the value you would get is zero, so A.
On the fourth question, the equation of the line perpendicular to line QR is y=2x+b, to find b, just substitute the point (5,6) to the equation. That would make b = -4. the final equation of the line would be: y=2x-4, so D.
On the fifth question, the equation of the line parallel to line QR is y = -2x + b. substitute the point (4,5) to the equation, and you'll get b = 13. the final equation of the line would be y=-2x+13, so A.

Mathematics

Line ab contains points a (1, 2) and b (−2, 6) the slope of line ab is a)zero b)undefined c)positive d)negative the equation of line cd is (y−3) = − 2 (x − 4). what is the slope of a line perpendicular to line cd? line cd contains points a (4, 6) and b (−2, 6). the slope of line cd is line qr contains (2, 8) and (3, 10) line st contains points (0, 6) and (−2, 2). lines qr and st are the equation of line qr is y = negative 1 over 2x + 1. write an equation of a line perpendicular to line qr in slope-intercept form that contains point (5, 6). the

Step-by-step answer

P Answered by Specialist

18

On the first question, the formula would be m=\frac{y2-y1}{x2-x1} and the value we got is -4/3, so D.
On the second quesiton, the slope in the given equation of the line is -2, its negative reciprocal is 1/2, so A.
On the third question, use the slope formula above and the value you would get is zero, so A.
On the fourth question, the equation of the line perpendicular to line QR is y=2x+b, to find b, just substitute the point (5,6) to the equation. That would make b = -4. the final equation of the line would be: y=2x-4, so D.
On the fifth question, the equation of the line parallel to line QR is y = -2x + b. substitute the point (4,5) to the equation, and you'll get b = 13. the final equation of the line would be y=-2x+13, so A.

Mathematics

Sara is trying to find an equation for a line that passes through (5, 2) and is perpendicular to 3x + 2y = 15. explain the steps that sara could take to determine the equation. a) write 3x + 2y = 15 in slope-intercept form. then, substitute the slope of that line and the point (5, 2) into the point-slope formula. b) write 3x + 2y = 15 in slope-intercept form. then, substitute the reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. c) write 3x + 2y = 15 in slope-intercept form. then, substitute the opposite reciprocal

Step-by-step answer

P Answered by Master

15

Option C)Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (5, 2) into the point-slope formula.

Mathematics

Sara is trying to find an equation for a line that passes through (5, 2) and is perpendicular to 3x + 2y = 15. explain the steps that sara could take to determine the equation. a) write 3x + 2y = 15 in slope-intercept form. then, substitute the slope of that line and the point (5, 2) into the point-slope formula. b) write 3x + 2y = 15 in slope-intercept form. then, substitute the reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. c) write 3x + 2y = 15 in slope-intercept form. then, substitute the opposite reciprocal

Step-by-step answer

P Answered by PhD

13

Not on your list, but an easy way is
.. a) swap coefficients of x and y, negating one. (Now you have 2x -3y.)
.. b) set any constant term to zero (now you have 2x -3y = 0)
.. c) translate the line to the point (5, 2) by substituting x ⇒ x-5, y⇒ y-2
2(x -5) -3(y -2) = 0

The way you've been taught, selection C is the proper choice.
Sara is trying to find an equation for a line that passes through (5, 2) and is perpendicular to 3x

Mathematics

Sara is trying to find an equation for a line that passes through (5, 2) and is perpendicular to 3x + 2y = 15. explain the steps that sara could take to determine the equation. a) write 3x + 2y = 15 in slope-intercept form. then, substitute the slope of that line and the point (5, 2) into the point-slope formula. b) write 3x + 2y = 15 in slope-intercept form. then, substitute the reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. c) write 3x + 2y = 15 in slope-intercept form. then, substitute the opposite reciprocal

Step-by-step answer

P Answered by Specialist

15

Option C)Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (5, 2) into the point-slope formula.

English

Which argument does the author use to support his or her position? a) large housing developments built on the mountains attract tourists to the region, boosting the economy. b) the citizens have urged the city council to encourage the development of large housing complexes on the mountains. c) the development poses a serious threat to the lives of people living downslope and to people living in the developments themselves. d) large housing developments built on steep slopes and along mountain ridges add to the scenic beauty of the region. ridgetop

Step-by-step answer

P Answered by PhD

C) The development poses a serious threat to the lives of people living downslope and to people living in the developments themselves.

Explanation:

This is the statement that best describes an argument used by the author to support his position. In this text, the author describes how he is against the creation of large housing developments built on the mountains. The author gives many reasons for this position, and one of them is the fact that the development poses a serious threat to the lives of people living downslope and to people living in the developments themselves.

English

Which argument does the author use to support his or her position? a) large housing developments built on the mountains attract tourists to the region, boosting the economy. b) the citizens have urged the city council to encourage the development of large housing complexes on the mountains. c) the development poses a serious threat to the lives of people living downslope and to people living in the developments themselves. d) large housing developments built on steep slopes and along mountain ridges add to the scenic beauty of the region. ridgetop

Step-by-step answer

P Answered by PhD

C) The development poses a serious threat to the lives of people living downslope and to people living in the developments themselves.

Explanation:

This is the statement that best describes an argument used by the author to support his position. In this text, the author describes how he is against the creation of large housing developments built on the mountains. The author gives many reasons for this position, and one of them is the fact that the development poses a serious threat to the lives of people living downslope and to people living in the developments themselves.

What is the slope of the line?

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