8. Write the equation of the line that is parallel, №18009909, 14.02.2020 13:36

Mathematics

8. Write the equation of the line that is parallel to the line 2x + 5y = 15 and passes through the point (-10, 1).

Step-by-step answer

P Answered by Specialist

$\sf y = \bold -\frac{2}{5} x -3$

Explanation:

part A identification for slope:

$\sf 2x + 5y = 15$

$\sf 5y = -2x + 15$

$\sf y = \frac{-2x + 15}{5}$

$\sf y = -\frac{2 }{5} x+3$

comparing with slope intercept form: y = mx + b

we can find that here the slope is $\bold -\frac{2}{5}$

part B, solving the equation:

if the line is parallel, then the slope will be same.

given coordinates: ( - 10, 1 )

using the equation:

y - y₁ = m( x - x₁ )

$\sf y - 1 = \bold -\frac{2}{5} (x --10)$

$\sf y = \bold -\frac{2}{5} x -4 + 1$

$\sf y = \bold -\frac{2}{5} x -3$

Extra information:

check the image below. this proves that the line is parallel and passes through point (-10, 1). the blue line is question line and red the answer line.

8. Write the equation of the line that is parallel to the line 2x + 5y = 15 and passes through the

Mathematics

Please help! (will give brainlist!) 37: given the line y=3/4x-2 a: find the parallel slope. b: find the perpendicular slope. 38: determine if the lines are parallel or perpendicular: a: -2x+5y=9 and 5x+2y=-6 b: 4y=8x+12 and -12x+6y=24 39: write an equation of a line that passes through (-4,-6) and is parallel to y=3x-8 40: write an equation of a line that passes through (2,5) and is perpendicular to y=1/4x-12

Step-by-step answer

P Answered by PhD

1

Step-by-step explanation:

Two lines are parallel if they have the same slope and are perpendicular if the product of their slopes is -1

37.a.Parallel slope=¾

b.Perpendicular slope =-1/¾=-4/3

38.a. -2x+5y=9 and 5x+2y=-6

For the first line,5y=2x+9,y=2/5x+9/5

For the second line,2y=-6-5x,y=-3-5/2x

Compare the slopes

2/5 vs -5/2 we see that -5/2 is the negative reciprocal of 2/5 therefore they are perpendicular

39. If both lines are parallel then their slopes are equal. The slope of y=3x-8 is 3

Using the point-slope form, y-y1=m(x-x1)

y--6=3(x--4)

y+6=3(x+4)

y+6=3x+12

y=3x+12-6

y=3x+6

40.The slope of y=¼x-12 is ¼

The negative reciprocal of it is the slope of it's perpendicular that is -1/¼=-4

Using the point slope form, y-y1=m(x-x1)

y-5=-4(x-2)

y-5=-4x+8

y=-4x+8+5

y=-4x+13

Mathematics

Please help! (will give brainlist!) 37: given the line y=3/4x-2 a: find the parallel slope. b: find the perpendicular slope. 38: determine if the lines are parallel or perpendicular: a: -2x+5y=9 and 5x+2y=-6 b: 4y=8x+12 and -12x+6y=24 39: write an equation of a line that passes through (-4,-6) and is parallel to y=3x-8 40: write an equation of a line that passes through (2,5) and is perpendicular to y=1/4x-12

Step-by-step answer

P Answered by PhD

1

Step-by-step explanation:

Two lines are parallel if they have the same slope and are perpendicular if the product of their slopes is -1

37.a.Parallel slope=¾

b.Perpendicular slope =-1/¾=-4/3

38.a. -2x+5y=9 and 5x+2y=-6

For the first line,5y=2x+9,y=2/5x+9/5

For the second line,2y=-6-5x,y=-3-5/2x

Compare the slopes

2/5 vs -5/2 we see that -5/2 is the negative reciprocal of 2/5 therefore they are perpendicular

39. If both lines are parallel then their slopes are equal. The slope of y=3x-8 is 3

Using the point-slope form, y-y1=m(x-x1)

y--6=3(x--4)

y+6=3(x+4)

y+6=3x+12

y=3x+12-6

y=3x+6

40.The slope of y=¼x-12 is ¼

The negative reciprocal of it is the slope of it's perpendicular that is -1/¼=-4

Using the point slope form, y-y1=m(x-x1)

y-5=-4(x-2)

y-5=-4x+8

y=-4x+8+5

y=-4x+13

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

1). write an equation of a line with the given slope and y-intercept. m= -2, b=4 a) y= -2x-4 b) y= -2x+4 c) y= -1/2x+4 d) y= 4x-2 2). find the slope and y-inercept of the line y= 1/5x-8 a). 5; 8 b). 8; 1/5 c). 1/5; -8 d). -8; 1/5 3). are the graphs of the lines in he pair parallel? explain y=6x+9 27x-3y=-81 a). yes, since the slopes are the same and the y-intercepts are the same. b). yes, since the slopes are the same and the y-intercepts are different. c). no, since the y-intercepts are different. 4). write y=3/5x+4 in a standard form using integers.

Step-by-step answer

P Answered by PhD

3

Answers:

1) The Equation of a Line is:

y=mx+b (1)

Where:

is the slope

is the y-intercept

For this problem we have a given m=-2 and a given b=4

So, we only have to substitute this values in the equation (1):

y=-2x+4

This is option B

2) Here we have to find the slope and the y-intercept of this equation:

$y=\frac{1}{5}x-8$

According to the explanation in the first answer related to the equation (1), the slope of this line is:

$m=\frac{1}{5}$

And its y-intercept is:

b=-8

This is option C

3) We have to Equations of the Line, and we are asked if these are parallel:

y=6x+9 (a)

27x-3y=-81 (b)

Equation (b) has to be written in the same form of (a), in the form y=mx+b in order to be able to compare both:

-3y=-81-27x

$y=-\frac{1}{3}(-81-27x)$

$y=\frac{81}{3}+\frac{27}{3}x$

y=9x+27 (c)

There is a rule that establishes that Two lines are parallel if they have the same slope. In this case, if we compare equations (a) and (c) we find they don’t have the same slope, then they are not parallel.

4) Here we are asked to write $y=\frac{3}{5}x+4$ in a standard form with integers:

$-\frac{3}{5}x+y=4$

Multiply each side by 5:

$5(-\frac{3}{5}x+y)=5(4)$

$5(-\frac{3}{5}x)+5y=20$

-3x+5y=20

In this case none of the options apply, please check if the question was written correctly.

5) In this question we are asked to write an equation parallel to:

y=2x+7 (2)

That passes through the given point (3,11). (Notice that in the Cartesian plane the points have an x-component and a y-component)

First, remember that two Equations of the line are parallel when they have the same slope. Now that this is clear, we are going to use the equation of the slope with the given point to find the parallel equation:

Equation of the slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ (3)

From (2) we know the slope is 2, then we only have to substitute this value and the points in (3):

$2=\frac{y-11}{x-3}$

2(x-3)=y-11

2x-6=y-11

Finally:

y=2x+5

This is option B

Mathematics

1). write an equation of a line with the given slope and y-intercept. m= -2, b=4 a) y= -2x-4 b) y= -2x+4 c) y= -1/2x+4 d) y= 4x-2 2). find the slope and y-inercept of the line y= 1/5x-8 a). 5; 8 b). 8; 1/5 c). 1/5; -8 d). -8; 1/5 3). are the graphs of the lines in he pair parallel? explain y=6x+9 27x-3y=-81 a). yes, since the slopes are the same and the y-intercepts are the same. b). yes, since the slopes are the same and the y-intercepts are different. c). no, since the y-intercepts are different. 4). write y=3/5x+4 in a standard form using integers.

Step-by-step answer

P Answered by PhD

3

Answers:

1) The Equation of a Line is:

y=mx+b (1)

Where:

is the slope

is the y-intercept

For this problem we have a given m=-2 and a given b=4

So, we only have to substitute this values in the equation (1):

y=-2x+4

This is option B

2) Here we have to find the slope and the y-intercept of this equation:

$y=\frac{1}{5}x-8$

According to the explanation in the first answer related to the equation (1), the slope of this line is:

$m=\frac{1}{5}$

And its y-intercept is:

b=-8

This is option C

3) We have to Equations of the Line, and we are asked if these are parallel:

y=6x+9 (a)

27x-3y=-81 (b)

Equation (b) has to be written in the same form of (a), in the form y=mx+b in order to be able to compare both:

-3y=-81-27x

$y=-\frac{1}{3}(-81-27x)$

$y=\frac{81}{3}+\frac{27}{3}x$

y=9x+27 (c)

There is a rule that establishes that Two lines are parallel if they have the same slope. In this case, if we compare equations (a) and (c) we find they don’t have the same slope, then they are not parallel.

4) Here we are asked to write $y=\frac{3}{5}x+4$ in a standard form with integers:

$-\frac{3}{5}x+y=4$

Multiply each side by 5:

$5(-\frac{3}{5}x+y)=5(4)$

$5(-\frac{3}{5}x)+5y=20$

-3x+5y=20

In this case none of the options apply, please check if the question was written correctly.

5) In this question we are asked to write an equation parallel to:

y=2x+7 (2)

That passes through the given point (3,11). (Notice that in the Cartesian plane the points have an x-component and a y-component)

First, remember that two Equations of the line are parallel when they have the same slope. Now that this is clear, we are going to use the equation of the slope with the given point to find the parallel equation:

Equation of the slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ (3)

From (2) we know the slope is 2, then we only have to substitute this value and the points in (3):

$2=\frac{y-11}{x-3}$

2(x-3)=y-11

2x-6=y-11

Finally:

y=2x+5

This is option B

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

Rewrite equation in slope intercept form, if necessary. Then determine whether the lines are parallel. Explain. 23. Y = -x + 6 24. Y - 7x = 6 25. 3x + 4y = 12 26. 2x + 5y = -1 x + y = 20 y + 7x = 8 6x + 2 = 6 10y = -4x - 20

Step-by-step answer

P Answered by Master

1

Step-by-step explanation:

Slope intercept form

y= mx + c

m=slope

c= intercept

1) y= -x + 6

2) y=7x + 6

3) y= -3/4x + + 3

4) y= -2/5x - 1/5

5) y= -x + 20

6) y= -7x + 8

7) y= -3x + 3

8) y= -2/5x -2

Line 1 and 5 are parallel because both have the same slope of -1

line 4 and 8 are also parallel as the their slopes are -2/5

Mathematics

1.write the equation of the line parallel to the line 10x - 5y = 8 and passing through the point (2, 2.write the equation of the line parallel to the line 4x + 2y = 5 and passing through the point (-3, 3.write the equation of the line parallel to the line 4x + y = -1 and passing through the point (5, 4.write the equation of the line perpendicular to the line x - 5y = -10 and passing through the point (2, 5.write the equation of the line perpendicular to the line x - 3y = 9 and passing through the point (3, . a.y = -5x + 15. b.y = 2x. c.y = -3x

Step-by-step answer

P Answered by PhD

8

1.) Parallel to 10x - 5y = 8 ; (2,4)

10x - 5y = 8
5y = 10x - 8
y = 2x - 8/5
m = 2

y - 4 = 2(x - 2)
y - 4 = 2x - 4
y = 2x

2.) Parallel to 4x + 2y = 5 ; (-3,5)

4x + 2y = 5
2y = -4x + 5
y = -2x - 5/2
m = -2

y - 5 = -2(x + 3)
y - 5 = -2x - 6
y = -2x -1

3.) Parallel to 4x + y = -1 ; (5,0)

4x + y = -1
y = -4x - 1
m = -4

y - 0 = -4(x - 5)
y = -4x + 20

4.) Perpendicular to x - 5y = -10 ; (2,5)

x - 5y = -10
5y = x + 10
y = x/5 - 2
m = -5

y - 5 = -5(x - 2)
y - 5 = -5x + 10
y = -5x + 15

5.) Perpendicular to x - 3y = 9 ; (3,5)

x - 3y = 9
3y = x - 9
y = x/3 - 3
m = -3

y - 5 = -3(x - 3)
y - 5 = -3x + 9
y = -3x + 14

8. Write the equation of the line that is parallel to the line 2x + 5y = 15 and passes through the point (-10, 1).

Step-by-step answer

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