I hate math like this

@Prometheus labs CEO
 
I think the things that looked at first like - signs are actually placeholders for fractions.
 
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.

Are the lone + and - signs meant to be 1 and -1, like in balanced ternary?

Yeah..

@BigBuggyBastage
 
I wasn’t aware mathematicians adopet programming “short cuts”. The more I learn!
 
Although, none would compile. Both -(x-) and (x+) are invalid operations.
 
 
@mathprofbrony  
Ah now I get it. I didn’t understand the “fill in part” the first time.
 
I thought I had realized what the teacher wants. like this:
 
-(x-) + 8 is  
-1**-1**(x**-1**-1) + 8  
Or just x+8.
 
But if it is like this, no answer is correct.
 
Soooo I’m team @mathprofbrony now. The only way for them to work is by completing the equations.

@mathprofbrony  
I’ll take a stab at this after my Adderall has kicked in, but I see where you’re coming from. I think my problem is that the ± and ∓ symbols exist; since the variable x is already defined, and assuming this is not multivariable algebra, the ‘blanks’ are confusing. Maybe the author of the problem didn’t have access to LaTeX or a normal word processor? I dunno. It’s 2019, not 1982, so that’d be kinda hard to believe.
 
 
Okay, let’s approach this quasi-graphically, i.e. determine the slope (m) by calculating rise / run:
 
m = (8-5) / [(1/2)(3/2)] = 3 / (-2) = -3/2 = -1.5
 
So the slope of a line connecting the given points is negative. Um…hopefully that helps. LoL
 
 
@Dsiak  
To play Devil’s Advocate for a minute, ____ and – are commonly used in “C-like” programming languages as increment and decrement operators, respectively. At a certain point in my own math career, the boundaries between math, algebra, calculus, etc. and programming becomes quite blurred, and often overlaps, because it’s easier to work with. Plus you end up using MATLAB, Octave, LabVIEW, SciLab, MathCAD, Maple, etc., anyway, so it’s faster to simply write out your notation as the prototype(s) of your program.
 
^{Ahh, MathCAD…you were my jam, until PTC purchased and ruined you…. :(}
 
But to the point, if we stay in the domain of Pure First-Year Algebra™, you’re correct. As mentioned, I’d have preferred/required the appropriate plus-minus/minus-plus symbols. AND, instead of these “empty fractions,” I’d like to see something other than what we’re interpreting as another minus operator symbol, e.g. empty brackets [], or even enumeration, e.g. x₁ x₂ for clarity.
 
EDIT: just saw another reply, I’ll have to update my response as required. :3

@Dsiak  

 
That’s just it. Notice that ____ isn’t there. It’s either a line - by itself, or + ~~, or ~~ -. I think that each time there, the line at the end is not a subtraction operator, but rather the line between the numerator and denominator of a fraction that the student is expected to fill in.

@mathprofbrony  
I can’t say I agree. I never saw it written like this.
 
I’m starting to think this can’t be considered an equation.
 
One can’t use an operator on an operator. ____ Doesn’t exist in math.
 
One could do something like (-x-y-z) But - is no more math then okey-dokey-loky is English.

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.

@BigBuggyBastage  
I agree.
 
If somepony write an equation like this you can just throw the equation away.
 
I honestly can’t read it. No clue what to do with these empty signs.

That notation is giving me a brain-ache.

 
Algebra hurts my head.

Where is Twilight when you need her.