What is the equation of this line in standard form (1 1/2,2) (-4,-1)

In general the line through (a, b) and (c, d) is

(c-a) (y-b) = (d-b) (x-a)

(-4 - 3/2) (y - 2) = (-1 - 2) (x - 3/2)

Multiply both sides by 2 to clear the fractions. We use the 2 in the first factor on the left and the second on the right.

(-8 - 3) (y-2) = (-3) (2x - 3)

-11 (y - 2) = - 3 (2x - 3)

-11y + 22 = - 6x + 9

6x - 11y = 9 - 22 = - 13

Answer: 6x - 11y = - 13

Check:

6 (1 1/2) - 11 (2) = 9 - 22 = - 13, good

6 (-4) - 11 (-1) = - 24 + 11 = - 13, good