In general terms, the equation of a line in slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
To transform the equation:
5x + 3y = 2
into slope-intercept form, you have to isolate y, as follows:
3y = 2 - 5x
y = 2/3 - 5/3x
where the slope is -5/3 and the y-intercept is (0, 2/3)