Bruce J. answered 12/09/18
Caltech/Johns Hopkins Grad with 15+ years of tutoring experience
The slope-intercept form of a line takes the form
y = mx + b
The value y = b (taken when x = 0) is called the y - intercept. The slope-intercept form of a line is unique.
With our line, (5/3)y = -(x-5), we can do some algebra to obtain
(5/3)y = -(x-5) -> y = -(3/5)(x-5) -> y = -(3/5)x + 3
This is the slope-intercept form, with m = -3/5 as the slope and b = 3 as the y-intercept.