How can I find the equation in standard form using only integers for the line through (-1,-3) and (2,-1)?

Answer 1

first find the slope
slope (-3 + 1)/(-1-2) = 2/3

using the point (2,-1)
y+1 = (2/3)(x-2)
3y+3 = 2x-4
2x - 3y = 7
or
2x - 3y - 7 = 0 , depending what your course defines as "standard from"

Answer 2

The slope is m = (-1 +3)/(2+1) = 2/3

So the equation in standard form is
y = (2/3)x + b
You still need to determine the constant b. Require that

-1 = (2/3)*2 +b
b = -7/3

Therefore
y = (2/3)x - 7/3

If you want integer coefficients only, you will have to write it as

3y = 2x - 7

Answer 3

Ax+By=C