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

6x - 11y = -13

Check:

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

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

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step-by-step explanation:

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