# Write the equation of the line parallel to y=2 and that has a y-intercept of -1

###### Question:

## Answers

y=-1

Step-by-step explanation:

The two lines are parallel,they have the same slope and slope=0

and the y-intercept is -1

so y=0x+(-1) y=-1

y=2/3x+5

Step-by-step explanation:y

=

2

3

x

+

5

Using the slope-intercept form, the slope is

2

3

.

m

=

2

3

To find an equation that is parallel to

y

=

2

3

x

+

5

, the slopes must be equal. Using the slope of the equation, find the parallel line using the point-slope formula.

(

0

,

0

)

m

=

2

3

Using the point-slope form

y

−

y

1

=

m

(

x

−

x

1

)

, plug in

m

=

2

3

,

x

1

=

0

, and

y

1

=

0

.

y

−

(

0

)

=

(

2

3

)

(

x

−

(

0

)

)

Solve for

y

.

y

=

2

3

x

y=2/3x

Step-by-step explanation: Find any equation parallel to the line.

Hope this helps you out! ☺

The correct option is

(B) [tex]y-(-1)=\dfrac{2}{3}(x-(-6)).[/tex]

Step-by-step explanation: Given that Audrey is trying to find the equation of a line parallel to [tex]y=\dfrac{2}{3}x-5[/tex] in slope-intercept form that passes through the point (-6, -1).

We are to find the equation of the line that she use.

The given line is

[tex]y=\dfrac{2}{3}x-5~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Comparing the above equation with the slope-intercept form [tex]y=mx+c,[/tex], we have

[tex]\textup{slope, m}=\dfrac{2}{3}.[/tex]

We know that the slopes of two parallel lines are equal.

So, the slope of the new line will also be

[tex]m=\dfrac{2}{3}.[/tex]

Since the line passes through the point (-6, -1), so its equation will be

[tex]y-(-1)=m(x-(-6))\\\\\\\Rightarrow y-(-1)=\dfrac{2}{3}(x-(-6)).[/tex]

Thus, the required equation of the line is

[tex]y-(-1)=\dfrac{2}{3}(x-(-6)).[/tex]

Option (B) is CORRECT.

Given the line with equation [tex]y=\dfrac{2}{3}x-5.[/tex]

Parallel lines have the same slopes, so the parallel line has equation

[tex]y=\dfrac{2}{3}x+a.[/tex]

This line passes through the point (-6,-1), then its coordinates satisfy the equation:

[tex]-1=\dfrac{2}{3}\cdot (-6)+a,\\ \\a=-1+4,\\ \\a=3.[/tex]

Therefore, the equation of needed line is

[tex]y=\dfrac{2}{3}x+3.[/tex]

y = - 9

Step-by-step explanation:

y = - 2 is a horizontal line parallel to the x- axis.

A parallel line must also be horizontal with equation

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through (7, - 9) with y- coordinate - 9, thus

y = - 9 ← equation of parallel line

y-(-1)=2/3 (x-(-6)

Step-by-step explanation:

So, we want to write an equation that is parallel to the original, and passes thru (-6,-1)... all that needs to be done is plug it in. Using the unsimplified slope intercept form, y-y1=m(x-x1), you will plug in the X and the Y. It will look like

y-(-1)=m (x-(-6), then since we want it to be parallel, you take the same slope from the other equation, because parallel lines never intersect. So then replace the "m" with "2/3". It should look like y-(-1)=2/3 (x-(-6).

A line parallel to y = 2/3 x - 5 will have a slope of 2/3.

The equation of a line passing through (-6, -1) with a slope of 2/3 is

y - (-1) = 2/3 (x - (-6))

Did u get anything? im also on this question

Parallel lines

the answer is y=2/3(x)+3