Graph the linear equation and answer each of the following questions. y> 2/3 x-2 what is the y-intercept? what is the slope (in fraction form)? is your slope positive or negative? explain how you plotted your second point

(i)

y-intercept is -2

(ii)

slope is

(iii)

slope is positive

(iv)

another point is (3,0)

Step-by-step explanation:

We are given equation as

now, we can compare it with slope intercept form of line

y=mx+b

where

m is slope

b is y-intercept

we get

So,

(i)

y-intercept is -2

(ii)

slope is

(iii)

we can see that

is a fraction and positive

so, slope is positive

(iv)

we can select any random value of x and find y

that will give us second point

Let's assume

x=3

So, another point is (3,0)

(v)

Graph:

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