I am totally ost please help?

Question

rewrite the equation 2x-3y= -6 as a function of x

Is it
a.) f(x)=3/2x-6
b.) f(x)=2/3x+6
c.) f(x)=3/2x-3
d.) f(x)=2/3x+2

Answer 1

f(x) is same as y value

so you should solve for y

i'll show the steps one by one

the equation is 2x-3y=-6

so first of all move 2x to the other side
like -3y=-2x-6

now you got only y but there's coefficient that bothers you
so now move -3 to the other side (-3will divide numbers on the left side cuz it's been related with y by mutiplication..)
so it would be like this
y=(-2x-6)/-3

which will be simplified as

y=2/3x+2

now you got the answer
f(x)=2/3x+2
which tells you d is the answer you'r looking for..

Answer 2

If c = 0, wecan solve for z and rewrite the plane as a function of two variables.Example 33 Find the function f (x, y) so that the plane 2x + 3y − z + 2 = 0
can be written as z= f (x, y). Sketch its graph using technology.We simply solve for z to obtainz= 2x + 3y + 2Thus, we havez= f (x, y) = 2x + 3y + 2The graph of this function is shown on figure 1.4.Figure 1.4: Plane2x + 3y − z = 2

Answer 3

To rewrite the equation as a function of x, it means to solve for y in terms of x.

2x - 3y = -6

Move the 2x over to the other side,

-3y = -2x - 6

Divide both sides by -3, to get

y = (2/3)x + 2

Therefore
f(x) = (2/3)x + 2

Answer 4

2x - 3y = -6
<=> 3y = 2x + 6
<=> y = 2/3 *x +2
thus d is the correct answer

Answer 5

2x-3y = -6

2x -3y = -6 ===> +6 =====> (2x - 3y) + 6 = -6 + 6
2x - 3y + 6 = 0 ===> +3y ====> (2x -3y + 6 ) +3y = +3y
2x + 6 = 3y ===> / 3 ===> ( 2x + 6 ) / 3 = 3y / 3
distribute 3 ===> 2/3x + 2 = y

Answer 6

This means solve for y in terms of x.

2x - 3y = -6
2x + 6 = 3y
3y = 2x + 6
y = (2/3)x + 2

The answer is d.

Answer 7

The answer to this one is to make it a y = equation

Therefore:
-3y = -6 -2x
y = 2 + 2/3x

or y = 2/3x + 2

which is d!

Answer 8

d