Question 1071591

Standard form is Ax + By = C   where A,B,and C are constants (often integers).

Point-slope form is  y = mx + b, where m=slope and b=y-intercept (i.e. value at x=0).

I've always found it easiest to work in point-slope form, then rearrange it to standard form at the end.   Given the two points, the slope can be found as rise/run (change in y value over change in x):
[ It does not matter which point you use as start/end, but once you decide which point to use as the "end", be sure to use the companion y value as the ending y value ]

             m = (y2-y1)/(x2-x1) 
             m = (3-0)/(0-(-8)) = 3/8

[ If we used the points the other way —> m = (0-3)/(-8-0) = -3/-8 = 3/8 ]

So far we have:
     y = (3/8)x + b

To find 'b', choose one of the points, say (-8,0), then plug in and solve for b:   
       0 = (3/8)(-8) + b  —>  0 = -3 + b —> b=3

        Now we have 
            y = (3/8)x + 3

 Re arranging to standard form:

                -(3/8)x + y = 3
              
Technically, the above is acceptable.  Some teachers may want you to make the coefficients integers if possible, and some *think* the coefficient in front of x should be positive (my Calculus book does not say this is a requirement).   So here are other forms that are equally valid:

Multiply through by 8:
             -3x + 8y = 24    (probably what most teachers expect)

Multiply through by -1:
               3x - 8y = -24   (some teachers may want to see it expressed like this, A>0)

Good luck!