The 2-point form of the equation for a line is

(y - y1) = ((y2 - y1)/(x2 - x1))*(x - x1)

Let (x1, y1) = (5, -4); (x2, y2) = (0, -7). Then we have

y -(-4) = ((-7 - (-4))/(0 - 5))*(x - 5) (plug in the numbers)

y + 4 = (-3/-5)*(x - 5) = (3/5)(x - 5) (simplify)

5y + 20 = 3x - 15 (multiply both sides by 5)

-3x + 5y = -35 (subtract 3x+20 from both sides)

3x - 5y = 35 (multiply both sides by -1)

Either of the last two versions is in standard form. I prefer the version with the fewest minus signs.

(y - y1) = ((y2 - y1)/(x2 - x1))*(x - x1)

Let (x1, y1) = (5, -4); (x2, y2) = (0, -7). Then we have

y -(-4) = ((-7 - (-4))/(0 - 5))*(x - 5) (plug in the numbers)

y + 4 = (-3/-5)*(x - 5) = (3/5)(x - 5) (simplify)

5y + 20 = 3x - 15 (multiply both sides by 5)

-3x + 5y = -35 (subtract 3x+20 from both sides)

3x - 5y = 35 (multiply both sides by -1)

Either of the last two versions is in standard form. I prefer the version with the fewest minus signs.