A line with a y - intercept of - 2 and an x - intercept of 3; in standard form

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