Mathematics: Write an equation in slope-intercept form for the line

Write an equation in slope-intercept form for, №15163195, 15.01.2021 00:59

Mathematics

Amira is told there is a trick to finding the slope within an equation in standard form, Ax+By=C. She is told she can rewrite this equation in slope-intercept form, y=mx+b, to find the pattern. She correctly rewrites the equation 7x+9y=14 in slope-intercept form as y=− 7/9x +14/9. Which answer explains the pattern for how to find the slope using an equation in standard form? A. In slope-intercept form, the slope is 14/9. These values are C and A, but with the opposite sign, so the slope of the line from the equation in standard form is − C/A. B.

Step-by-step answer

P Answered by PhD

4

B. In slope-intercept form, the slope is − 7/9. These values are A and B, but with the opposite sign, so the slope of the line from the equation in standard form is − A/B.

Step-by-step explanation:

Let's convert the standard equation into slope-intercept form:

Ax + By = C ⇒ subtract Ax from both sidesBy = -Ax + C ⇒ divide both sides by By = -A/Bx + C/B ⇒ converted to slope- intercept form

As we see the slope is -A/B

The equation 7x + 9y = 14 is converted as:

y = -7/9x + 14/9, where the slope is -7/9

Looking at the answer options and the correct one is option B, where both identification of slopes match.

B. In slope-intercept form, the slope is − 7/9. These values are A and B, but with the opposite sign, so the slope of the line from the equation in standard form is − A/B.

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

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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

Amira is told there is a trick to finding the slope within an equation in standard form, Ax+By=C. She is told she can rewrite this equation in slope-intercept form, y=mx+b, to find the pattern. She correctly rewrites the equation 7x+9y=14 in slope-intercept form as y=− 7/9x +14/9. Which answer explains the pattern for how to find the slope using an equation in standard form? A. In slope-intercept form, the slope is 14/9. These values are C and A, but with the opposite sign, so the slope of the line from the equation in standard form is − C/A. B.

Step-by-step answer

P Answered by PhD

4

B. In slope-intercept form, the slope is − 7/9. These values are A and B, but with the opposite sign, so the slope of the line from the equation in standard form is − A/B.

Step-by-step explanation:

Let's convert the standard equation into slope-intercept form:

Ax + By = C ⇒ subtract Ax from both sidesBy = -Ax + C ⇒ divide both sides by By = -A/Bx + C/B ⇒ converted to slope- intercept form

As we see the slope is -A/B

The equation 7x + 9y = 14 is converted as:

y = -7/9x + 14/9, where the slope is -7/9

Looking at the answer options and the correct one is option B, where both identification of slopes match.

B. In slope-intercept form, the slope is − 7/9. These values are A and B, but with the opposite sign, so the slope of the line from the equation in standard form is − A/B.

Mathematics

1. write and equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (2,-2); y=-x-2 a)y=-2x b)y=2x c)y=1/2x d)y=-x 2. write and equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (2,-1); y=-3/2x+6 a)y=-3/2x+1 b)y=-3/2x-1 c)y=-3/2x+2 d)y=-3/2x+4 3. write and equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.

Step-by-step answer

P Answered by PhD

6

1. The correct option is D.

2. The correct option is C.

3. The correct option is D.

4. The correct option is B.

5. The correct option is D.

Step-by-step explanation:

The slope intercept form of a line is

y=mx+b

where, m is slope and b is y-intercept.

The slope of parallel lines are same.

(1)

The required line is parallel to the line y=-x-2 and passes through (2,-2). Slope of the line is -1.

The equation of required line is

y-y_1=m(x-x_1)

y-(-2)=-1(x-2)

y+2=-x+2

y=-x

Therefore the correct option is D.

(2)

The required line is parallel to the line y=-3/2x+6 and passes through (2,-1). Slope of the line is -3/2.

The equation of required line is

y-y_1=m(x-x_1)

$y-(-1)=-\frac{3}{2}(x-2)$

$y+1=-\frac{3}{2}x+3$

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

Therefore the correct option is C.

(3)

The required line is parallel to the line x=-3 and passes through (4,2). Slope of the line is infinite.

The equation of required line is

y-y_1=m(x-x_1)

$y-2=\frac{1}{0}(x-4)$

0=x-4

x=4

Therefore the correct option is D.

(4)

Product of slopes of perpendicular lines is -1.

The required line is perpendicular to the line y=1/2x-1 and passes through (-2,3). Slope of the required line is -2.

The equation of required line is

y-y_1=m(x-x_1)

y-3=-2(x-(-2))

y-3=-2x-4

x=-2x-1

Therefore the correct option is B.

(5)

The required line is perpendicular to the line y+1=2(x-3) and passes through (5,0). Slope of the required line is -1/2.

The equation of required line is

y-y_1=m(x-x_1)

$y-0=-\frac{1}{2}(x-5)$

$y=-\frac{1}{2}(x)+\frac{5}{2}$

Therefore the correct option is D.

Mathematics

Me with this set of 1.write an equation in point-slope form for the line that has a slope of 9/4 and contains the point (3, −4). 2. identify the equation in slope-intercept form for the line containing the points (3, 5) and (2, −5). 3. write an equation in slope-intercept form for the line perpendicular to y = −4x + 1 that passes through the point (−7, 1). 4. describe the transformation from the graph of f(x) to the graph of g(x). f(x) = 4x, g(x) = −4x 5. identify the equation that describes the line in slope-intercept form. slope = 3, point (−2,

Step-by-step answer

P Answered by PhD

2

1. Y = 94x-39/4

2. Y = 10x-25

3. Y = 1/4x

4. Graph moves 8 units to the left

5. Y=3x+2

Mathematics

1. write and equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (2,-2); y=-x-2 a)y=-2x b)y=2x c)y=1/2x d)y=-x 2. write and equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (2,-1); y=-3/2x+6 a)y=-3/2x+1 b)y=-3/2x-1 c)y=-3/2x+2 d)y=-3/2x+4 3. write and equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.

Step-by-step answer

P Answered by PhD

6

1. The correct option is D.

2. The correct option is C.

3. The correct option is D.

4. The correct option is B.

5. The correct option is D.

Step-by-step explanation:

The slope intercept form of a line is

y=mx+b

where, m is slope and b is y-intercept.

The slope of parallel lines are same.

(1)

The required line is parallel to the line y=-x-2 and passes through (2,-2). Slope of the line is -1.

The equation of required line is

y-y_1=m(x-x_1)

y-(-2)=-1(x-2)

y+2=-x+2

y=-x

Therefore the correct option is D.

(2)

The required line is parallel to the line y=-3/2x+6 and passes through (2,-1). Slope of the line is -3/2.

The equation of required line is

y-y_1=m(x-x_1)

$y-(-1)=-\frac{3}{2}(x-2)$

$y+1=-\frac{3}{2}x+3$

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

Therefore the correct option is C.

(3)

The required line is parallel to the line x=-3 and passes through (4,2). Slope of the line is infinite.

The equation of required line is

y-y_1=m(x-x_1)

$y-2=\frac{1}{0}(x-4)$

0=x-4

x=4

Therefore the correct option is D.

(4)

Product of slopes of perpendicular lines is -1.

The required line is perpendicular to the line y=1/2x-1 and passes through (-2,3). Slope of the required line is -2.

The equation of required line is

y-y_1=m(x-x_1)

y-3=-2(x-(-2))

y-3=-2x-4

x=-2x-1

Therefore the correct option is B.

(5)

The required line is perpendicular to the line y+1=2(x-3) and passes through (5,0). Slope of the required line is -1/2.

The equation of required line is

y-y_1=m(x-x_1)

$y-0=-\frac{1}{2}(x-5)$

$y=-\frac{1}{2}(x)+\frac{5}{2}$

Therefore the correct option is D.

Mathematics

PLEASE HELP The Scenario:You want to start your own 3-D printing and manufacturing business. Use what you know about shifting functions to plan your business and find a profitable model. 1. What are you going to make? (The maximum build size is 25 cm by 16 cm by 15 cm) I’m going to make a small organizer for office. Like an empty cube 6cm by 6 cm by 6 cm 2. For each expense category – complexity, design, and quality – decide whether your product has high, medium, or low requirements. In the table below, fill in the three boxes that apply to your

Step-by-step answer

P Answered by Specialist

10

can I answer your question in comment box

Mathematics

Will get brainiest and 50 2. suppose y varies directly with x, and y = 15 and x = 5. write a direct variation equation that relates x and y. what is the value of y when x = 9? 3. write an equation in slope-intercept form of the line that passed through (-3, 4) and (1. 4). 4. use point-slope form to write the equation of a line that has a slope of 2/3 and passes through (-3, -1). write your final equation in slope-intercept form. 5. write the equation in standard form using integers (no fractions or decimals): = −2/3 − 1 6. write an equation of

Step-by-step answer

P Answered by Specialist

10

When

varies directly with

, the equation for the line will be y=kx

(called direct variation). It represents that

is the result of

being modified and nothing else being added or subtracted. Here's the math:

2. Suppose

varies directly with

and

and

. Write a direct variation equation that relates

and

. What is the value of

when

?

replace

and

with the given values in a direct variation equation

y=kx

solve for

(direct variation)

k=3

the equation for the line is y=3x

, now solve for

when

3. Write an equation in slope-intercept form of the line that passed through (-3,4)

and

.

write the expression for slope when y=mx+b

$m= \frac{ y_{2} - y_{1} }{x_2- x_{1} }$

define variables

$y_{2} =4 \\ y_{1} =4 \\ x_{2} =1 \\ x_{1} =-3$

insert values into slope expression

$m= \frac{ 4- 4}{1- (-3) }$

simplify

m=0

now, plug in the slope into the equation y=mx+b

solve for

, plug in an

and

value from the given coordinate (-3,4)

4. Use point-slope form to write the equation of a line that has a slope of 2/3

and passes through (-3,-1)

. Write your final equation in slope-intercept form.

write the point slope form equation from the slope intercept form equation

$y=mx+b \\ y- y_{1} =m(x- x_{1} )$

replace $y_{1}$ with

and $x_{1}$ with

simplify

insert the slope for

simplify

5. Write the equation in standard form using integers: y=-2/3x-1

standard form is Ax+By=C

, so rearrange the variables into that form

y=-2/3x-1

multiply both sides by

6. Write an equation of the line that passes through (2,-1)

and is parallel to the graph of y=5x-2

. Write your final equation in slope-intercept form.

parallel lines have the same slope, but different y-intercepts

to solve for the y-intercept of the second line, replace x and y with given values

-1 = 5(2) + b

ANSWERS:

2. y=3x

and

when

3.

4.

5.

6.

Hope this helps! I have added the answer to Question #5!

Mathematics

Me with this set of 1.write an equation in point-slope form for the line that has a slope of 9/4 and contains the point (3, −4). 2. identify the equation in slope-intercept form for the line containing the points (3, 5) and (2, −5). 3. write an equation in slope-intercept form for the line perpendicular to y = −4x + 1 that passes through the point (−7, 1). 4. describe the transformation from the graph of f(x) to the graph of g(x). f(x) = 4x, g(x) = −4x 5. identify the equation that describes the line in slope-intercept form. slope = 3, point (−2,

Step-by-step answer

P Answered by PhD

2

1. Y = 94x-39/4

2. Y = 10x-25

3. Y = 1/4x

4. Graph moves 8 units to the left

5. Y=3x+2

Mathematics

Will give brainiest and 60 points if you show work so i can understand these. 1. find the slope of the line that passes through the points (-1, 2), (0, 5). 2. suppose y varies directly with x, and y = 15 and x = 5. write a direct variation equation that relates x and y. what is the value of y when x = 9? 3. write an equation in slope-intercept form of the line that passed through (-3, 4) and (1. 4). 4. use point-slope form to write the equation of a line that has a slope of 2/3 and passes through (-3, -1). write your final equation in slope-intercept

Step-by-step answer

P Answered by Specialist

8

1) use change in y/change in x to find the slope from two points:

change in y: 5-2=3

change in x: 0-(-1)=1

3/1=3 is your slope

2) if it is a direct variation, you know as x increases, y increases, both at constant rates

since y is 10 more than x in the example, it will always be 10 more than x

y=x+10 is your equation.

when x=9, y=19

now they could not be reffering to their difference in addition, but their difference in multiplication. In that case, y is 3 times x in the example, so it will always be 3 times x

y=3x is your equation

when x=9, y=27

3) the slope of this line is determined by change in y over change in x:

change in y: 4-4=0

you don't need to calculate the change in x because 0 divided by anything is 0, so that is your slope.

y=0x+b

4=0(1)+b

4=0+b

4=b

y=4 is your equation because 0 times x is zero. this means that it is a horizontal line with a constant y value of 4

4)

y - value of y in a point =slope (x - value of x in a point)

y-(-1)=2/3 * (x-(-3))

y+1=2/3x+2/3(3)

y+1= 2/3x+2

y=2/3x+1

from solving point slope form, you can get to slope intercept form

5) not sure what this question is asking for

- a line?

- an expression equivalent to -1 and 2/3?

both of those aren't possible with the information given

6) parallel means same slope different y intercept

y=5x+b

-1=5(2)+b

-1=10+b

-11=b

y=5x-11

Write an equation in slope-intercept form for the line

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