What is the equation of this line in standard form?

First find the slope, m:
   
          2-(-1)              3
m = = = 6/7
        (1/2)-(-3)         3.5

Now use the slope-intercept formula:

y = mx + b

Choosing the point  (1/2, 2),    2 = (6/7)(1/2) + b.  Find b (the y-intercept):

14 [ 2 = (6/7)(1/2) + b ]  =>  28 = 6 + 14b.

Then 22 = 14b, and b = 22/14.

Then the eqn of the line is y = (6/7)X + 22/14

Mult. all terms by 14 to remove the fractions:

14y = 12x + 22

Finally, rearrange the terms:  -12x + 14y - 22 = 0.  This is the eqn in standard form, as requested.