Question

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20 points
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Answer 1

The slope-intercept form of the equation is,

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

Explanation:

The given equation is

`3x+y=-8`

Let us make y the subject to obtain,

`y=-3x-8`

The slope of this line is
`-3`.

The slope of the line perpendicular to this line should have a slope that is the negative reciprocal of
`-3`.

The slope of the perpendicular line is

`= (-1)/(-3)=(1)/(3)`

The slope-intercept form of a line is given by

`y=mx+c`, where
`m=(1)/(3)`. We substitute this into the equation to obtain,

`y=(1)/(3)x+c`

Since the line passes through
`(-3,1)`, it must satisfy its equation.

This implies that,

`1=(1)/(3)(-3)+c`

This simplifies to,

`1=-1+c`

`1+1=c`

`2=c`

We substitute all these values into the equation to get,

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

Answer 2

y = 1/3x+2

Explanation:

3x+y = -8

This need to be in slope intercept form, y = mx+b

Subtract 3x from each side

y = -3x-8

The slope is -3

If we want our line to be perpendicular, the slope must be a negative reciprocal.

Take -3, negate it and flip it

-(-1/3) = 1/3

The slope of a perpendicular line is 1/3

We have the slope and a point (-3,1)

We can use point slope form to make a line

y-y1 = m(x-x1)

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

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

Distribute

y-1=1/3x+1

Add 1 to each side

y-1 +1= 1/3x+1+1

y = 1/3x+2

This is in slope intercept form