Question

What is the standard form of the equation of the line through (6,-3) with a slope of 2/3

Answer 1

Y-y1 = m(x-x1)
y+3 = 2/3(x-6)
y+3 = 2/3 x -4
y = 2/3 x -7
mult both sides by 3 to get rid of the fraction so. 3y=2x - 7

then put in proper order

2x - 3y = 7

Answer 2

Ax+by=c is the standard form
you are given the slope and a point, so first write the equation in point-slope form:
y-(-3)=2/3(x-6)
expand the equation: y+3=(2/3)x-4
(2/3)x-y=7 is the standard form