@AspectofBlood21
 
@Penguinbrony24
 
…huh? There’s no FOIL here. FOIL is “First Outer Inner Last.” It’s a method of multiplying binomials. This is just a problem of calculating the equation of a line using the point-slope form.
 
As I commented on another version of this picture, which should really be merged:
 
I think the things that looked at first like — signs are actually placeholders for fractions. (The line in the middle of a fraction is called the vinculum.)
 
The answer to the question is
 
f(x) = — 3/2 (x — 3/2) + 5
 
which is answer D.
 
The slope of the line is rise/run, which is (5 — 8) / (3/2 — (-1/2)) = -3/2. So the slope is negative, which means the answer is C or D.
 
C and D both involve subtracting a positive fraction, so of the two points, you’ll choose the 3/2 x-value. At that point, the y-value is 5. That gives answer D.
 
An equivalent form of the equation would be
 
f(x) = -3/2(x + 1/2) + 8
 
but that would require an additional negative sign in front of answer A.
 
I don’t really like the format of this question because it’s perfectly possible to have a fraction in which the numerator is a negative number: for instance, you could claim
 
f(x) = (-3)/2 (x + 1/2) + 8
 
was the equation and that would be completely correct. But I think that this question is separating negative signs and using the fractional vinculum to show students where to write their numbers.

@Penguinbrony24  
^this

Those graphing problems are easy enough as you can use foil to factor and figure it out. The one above isn’t that hard if you’ve got a graphing calculator.

Give up now while you still can

I assume these two will be merged, but as I said on the other:
 
I think that two of the “dashes” are not minus signs, but the vinculum of a fraction. I believe the requirement here is to:
 
*) choose whether the slope is positive or negative;  
*) choose whether the quantity within the parentheses is (x+ *) or (x - *), where _ is a positive fraction; and  
*) fill in the required fraction for the slope and an initial x-value as + _ or - *, where * is a positive fraction.

These ain’t so bad. Off the top of my head, we are looking for slope to solve this.

Come on. I’m garbage at math and even I can solve these…

Can you not give me trig class PTSD?