Write an equation that represents the line use exact numbers

The equation that represents the line using exact numbers is and this can be determined by using the point-slope form.

Given :

Points - (0,-1) and (3,-5)

To determine the equation of a line, a point-slope form of the line can be used. The point-slope form is given by the equation:

  ---- (1)

where, and are the points on the line.

Now, put the values of   and in the equation (1).

The equation that represents the line using exact numbers is .

For more information, refer to the link given below:

link

y = (-6/7)x - 1

Step-by-step explanation:

There's a dot where this line crosses the y-axis; it's represented by the point (0, -1).  Consequently, the y-intercept, b, of this line is -1.

As x increases from -6 to 0, y decreases from 7 to -1.  The change in x is 7 units and the change in y is -6 units.  Thus, the slope of this line is

m = rise / run = -6 / 7.

Again, the y-intercept is b = -1.

Thus, inserting the knowns into the slope-intercept form of the equation of a straight line results in:

y = (-6/7)x - 1

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