Question

(4,7)(-12,3) into standard form

Answer 1

You seem to be sharing two points:  (4,7)(-12,3).
But you don't explain what you're looking for.

I must assume you want to find the equation of the str. line thru these 2 pts, in std. form.    Ax+By+C=0.

1.  Find the slope of the line thrugh (4,7)(-12,3):  rise is -4 and run is -16.
   Thus the slope is -4/16, or -1/4.
2.  Write out the slope-intercept equation of this line:  subst. m = -1/4 and the coordinates of either given point:

   y = mx + b         becomes  y = (-1/4)x + b

Let's subst. 4 for x and 7 for y:     7 = (-1/4)(4) + b, or
                                                    7 = -1 + b.  Then b = 8.

Convert this to the equation in std. form:

y = (-1/4)x + 8     Mult all three terms by 4 to eliminate fractions.

4y = -x + 32, or 0 = -4y -x + 32, or 4y + x - 32 = 0   (answer)