The slope-intercept form: y = mx + b
m - slope
b - y-intercept
We have y-intercept b = -2, therefore y = mx - 2.
The x-intercept = 3 is for y = 0. Substitute:
0 = m(3) - 2 add 2 to both sides
2 = 3m divide both sides by 3
m = 2/3
Therefore y = 2/3 x - 2.
The standard form: Ax + By = C.
2/3 x - 2 = y add 2 to both sides
2/3 x = y + 2 subtract y from both sides
2/3 x - y = 2 multiply both sides by 3
2x - 3y = 6