Write an equation in standard form for the line that passes through the given points.
(0,6) and (4.0)

The equation of the line in standard form is

Step-by-step explanation:

we know that

The equation of the line in standard form is

where

A is a positive integer

B and C are integers

step 1

Find the slope of the line

The formula to calculate the slope between two points is equal to

we have the points

(0,6) and (4.0)

substitute the values

step 2

Find the equation of the line in slope intercept form

where

m is the slope

b is the y-coordinate of the y-intercept

we have

Remember that the y-intercept is the value of y when the value of x is equal to zero

In this problem the y-intercept is given

The y-intercept is the point (0,6)

so

substitute

step 3

Convert to standard form

Multiply by 2 both sides to remove the fraction

Adds 3x both sides

c

step-by-step explanation:

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2