GEOMETRY

y=-2. 

Because the line is horizontal, the slope is undefined. 

The slope of a horizontal line is well defined- it is zero.

I think what is wanted is as follows:

General equation of a straight line is y =mx + c

Here we know that this line goes through point (3, -2) so we can say

-2 = m*3 + c

This means c = -2 - 3m.  Put this in the equation for the line:

y = mx - 2 - 3m

or

y = m(x - 3) - 2

The slope m is undefined.

To put it simply, in linear equations, if an equation is y= (any real number), then it is horizontal. For example, y=2 is horizontal, and it has an undefined slope. x=3 is actually a vertical line. Its slope is 0.

Correct me if I'm wrong. 

BOSEOK is correct; the equation is x=3.

Contrary to what Gh0sty stated, the slope is defined when a linear function happens to be horizontal. Let's figure out the slope of the graph provided by Gh0sty. I will use the points $(3,-2)$ and $(0,-2)$. Let's find the slope.

Of course, the formula for slope is the following:

$m=\frac{y_2-y_1}{x_2-x_1}$

The slope is 0. 0 is a valid number for the slope. If you type into Demos y=0x-2, the line will appear exactly as the picture above. 

Let's try calculating the slope of the line x=-3. Two arbitrary points on the line are $(-3,2)$ and $(-3,0)$

What is the slope of this? Let's try using the formula again. Let's see what happens.

Of course, any number divided by 0 is undefined and therefore it has an undefined slope. 

Therefore, BOSEOK's answer is correct because it meets both criteria of

1) A line with an undefined slope

2) A line that passes through the point $(3,-2)$

And therefore, $x=3$ is correct.