Respuesta :

wegnerkolmp2741o

Answer:

y = 1/3x+2

Step-by-step 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

kudzordzifrancis

Answer:

The slope-intercept form of the equation is,

[tex]y=\frac{1}{3}x+2[/tex]

Step-by-step explanation:

The given equation is

[tex]3x+y=-8[/tex]


Let us make y the subject to obtain,


[tex]y=-3x-8[/tex]


The slope of this line is [tex]-3[/tex].


The slope of the line perpendicular to this line should have a slope that is the negative reciprocal of [tex]-3[/tex].


The slope of the perpendicular line is

[tex]= \frac{-1}{-3}=\frac{1}{3}[/tex]


The slope-intercept form of a line is given by


[tex]y=mx+c[/tex], where [tex]m=\frac{1}{3}[/tex]. We substitute this into the equation to obtain,


[tex]y=\frac{1}{3}x+c[/tex]


Since the line passes through [tex](-3,1)[/tex], it must satisfy its equation.


This implies that,

[tex]1=\frac{1}{3}(-3)+c[/tex]


This simplifies to,


[tex]1=-1+c[/tex]


[tex]1+1=c[/tex]


[tex]2=c[/tex]


We substitute all these values into the equation to get,

[tex]y=\frac{1}{3}x+2[/tex]