What is the answer for this equation to put it in slope-intercept formula: y-2=-5/3(x-4)

Since you have a denominator of 3, multiply 3 times both sides:

3[y - 2]  =  3[ -5/3(x - 4) ]               When you multiply by 3, multiply only the first factor, not both of them.

3y - 6  =  -5(x - 4)                           Use distributive property.

3y - 6  =  -5x + 20                          Add 6 to both sides.

3y  =  -5x + 26                               Divide both sides by 3.

y  =  (-5/3)x + (26/3)