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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

The slope-intercept form of the equation is,

Step-by-step explanation:

The given equation is

Let us make y the subject to obtain,

The slope of this line is .

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

The slope of the perpendicular line is

The slope-intercept form of a line is given by

, where . We substitute this into the equation to obtain,

Since the line passes through , it must satisfy its equation.

This implies that,

This simplifies to,

We substitute all these values into the equation to get,

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)