Given Y-6=3(x-1/3), we want the slope-intercept form, y = mx + b, where b is the y-intercept.
Multiplying out 3(x - 1/3), we get 3x - 1. Then
Y-6=3(x-1/3) => y-6 = 3x - 1
Adding 6 to both sides, we get:
y = 3x +5
This is in slope-intercept form. The slope is m = 3 and the y-intercept is b = 5.