1. x| -5,-3,0,2
   y| 32,21,7,-3

(-5,32), (-3,21), (0,7), (2,-3)

Let's plot them, connect them, then connect the first 
point to the last point and see if they 

(a) all fall on a line, and,
(b) if they fall on a line, the line that they fall on 
    that has a y-intercept of 7, and 
(c) if they fall on a line with a y-intercept of 7, the 
    line that they fall on has a slope of -5:



No, they don't quite fall on the same line, as we can see
when we draw a black line from the first point to the last 
one in the second graph above, because (-3,21) sticks out a
little too far to the left.
 
-------------

2. x| -5,-3,0,2
   y| 32,22,6,-3

(-5,32), (-3,22), (0,6), (2,-3)

Let's do the same with these:



No, they don't quite fall on the same line, as we can see
when we draw a black line from the first point to the last 
one in the second graph above, because (0,6) sticks out a 
little too far to the left.  [Besides, it would have to cross
the y-axis at (0,7)].

---------------

3. x| -5,-3,0,2
   y| 32,22,7,-3

(-5,32), (-3,22), (0,7), (2,-3)

Let's do the same with these:



Well these do fall on the same line, as we can see
when we draw a black line from the first point to the last one
in the second graph above the black line falls right on top of
the red,green, and blue parts.  Also it does have y-intercept
at 7.  But we must check to see if its slope is -5. We consider
the slope to be -5/1, so in the third graph above, we drew a 
line from the y-intercept (0,7) straight down the y-axis 5 units 
and then right 1 unit, and we ended up right on the line and now
we know that this is the correct answer.
 
There is no use to do (4), because we have already found the
right answer, but we will do it anyway, just to follow through.


4. x| -5,-3,0, 2
   y| 32,22,7,-5

(-5,32), (-3,22), (0,7), (2,-5)




No, they don't quite fall on the same line, as we can see
when we draw a black line from the first point to the last 
one in the second graph above, because (2,-5) is too far
down.

But this is not the way you're supposed to do the problem.
You're supposed to use the slope formula to find all 3
slopes of the three parts of each one and find the one
that has all three slopes equal to -5 and that passes
through (0,7).  The correct choice will, of course, be 3.

Edwin